UK National Newspapers
Many local libraries offer in-home access to a database called Newsbank, which includes most current national and some regional dailies - plus a few local weeklies. This is text-only and generally only covers the past fifteen years or so, although their databases for The Independent, Daily/Sunday Mirror and The People go back to 1992, the Daily Record/Sunday Mail to 1994, The Sun to 1996, the Financial Times to 1982 and The Times/Sunday Times to 1985. Check your local library website!
The Times runs its own paid-for archive, but this now only seems to be available as part of a subscription to the newspaper itself: http://www.thetimes.co.uk/tto/archive/
However, most public libraries within the UK offer free at-home online access to The Times Digital Archive through Gail/Cengage. This archive does not include the Sunday Times - although Gail/Cengage do offer this to libraries as a separate product: I don't actually know of a library which subscribes to it, though. See also Newsbank above. Check your local library website!
The Daily Telegraph
Recent (October 2000 onwards) issues of both the daily and Sunday papers are on Newsbank, but there is no full archive of the Telegraph available online. However, since the beginning of 2014 they have been making issues from exactly 100 years ago available for free download as PDFs on their website. This is a continuing project with a new issue to be added every day until the end of 2018! (There was no Sunday Telegraph until 1961, so there are only six per week.) You can find the index page here: http://www.telegraph...ws/ww1-archive/
The Guardian/The Observer
Some public libraries offer free at-home access to The Guardian's archive, but they are very much in the minority. Recent issues (1998 onwards) are on Newsbank. For those without free access, it is possible to buy daily, three-day and monthly passes through Pro-Quest: http://pqasb.pqarchi...ian/offers.html
UK Press Online
This multi-paper archive is available free in some public libraries and most academic libraries. The main national papers included are the Daily Mirror and Daily Express, but it also includes such quirky titles as the Daily Worker and various Mosleyite papers from the 1930s: surprisingly you can sometimes find motor sporting news - and even race reports - in these! The World War 2 collection also includes the Yorkshire Post 1933-45. UK Press Online also offers day, five-day and 90-day passes with unlimited downloads: I managed several hundred on a day pass! (Handy hint: a day pass here can theoretically last anything up to 48 hours, since it expires at midnight the day after you make the purchase!)
Like the Sunday Times, the Daily Mail is available to public libraries via Gale/Cengage. Again, I don't know of a library which offers it - but presumably there must be some somewhere!
UK REGIONAL PAPERS
British Newspaper Archive
The BNA is an ongoing project, using the British Library's collections, with new material added almost daily. It includes regional dailies, evening papers and weeklies, mostly from England and Scotland, but with a few Welsh and Irish titles. Much of it is based on an earlier BL project which was focused on pre-20th century papers and which is sometimes offered free by public libraries through Gale/Cengage as 'Nineteenth Century Newspapers', but it is now being expanded into the mid-20th century.
Anyone researching pre-war Donington Park events will be able to find original reporting from - for example - the Nottingham Evening Post. I'm sure there's much more to find there.
Searching is free and the search engine is quite good, but until recently it wasn't cheap to use. However, they have recently introduced an extremely good value monthly pass which offers unlimited PDF downloads for just £9.95.
ISLE OF MAN
The Manx Museum's collection of newspapers is available online. You will need to create a user account with the Manx government website, but once you have done that it is free to search the database, with various pass options available for downloads. Bike racing fans may be interested to note that the entire 1930-1961 archive of TT Special - the paper produced only during TT and Manx GP weeks - is available.
Click on 'Manx National Heritage': https://www.gov.im/onlineservices/
I believe some Scottish libraries offer free access to The Scotsman archive. The rest of us have to make do with paying for it! The archive only goes to 1950, with access via an annual, monthly, weekly or two-day pass.
The Glasgow Herald is - as far as I'm aware - one of only two 20th century British newspapers available in Google News Archive. It was never searchable, but you can browse it on the link below. The archive ends in early 1990.
The other 20th century British paper in Google News. Not searchable and covering 1951-91 only.
Welsh Newspapers Online
Provided by the Welsh National Library - and still in beta - WNO includes a large number of daily and weekly Welsh papers - in both Welsh and English. At least at present, the archive ends at 1919, with the majority of the papers being pre-Great War. But it's a start. And it's free!
This archive also includes the Irish Times Weekly. Searchable for free, but you need to buy a pass to download articles. The weekly motoring column often covered sporting matters.
Irish News Archive
Includes the daily Irish Independent, together with a number of regional papers from all across Ireland. Again free to search, with one- and two-day, weekly, monthly and annual passes available.
Just released - the complete archive of Motor Sport back to 1924. See this thread for a few further details.
The whole archive of Karting Magazine is online - free - on the link below:
While this magazine might not seem immediately obvious as a source, it sometimes comes up trumps on the most unlikely things. It taught me a lot about Pneugrippa machines - among other things - and you can find interesting snippets about drivers and entrants with trade connections. Even the occasional article by WB! There are page viewing limits, but these can be easily circumvented.
Illustrated London News
Another Gail/Cengage offering, which is available through some public libraries. Often covered motoring subjects - occasionally sporting-related.
Also available through Gail/Cengage - although surprisingly few libraries seem to offer it, given its iconic status throughout the 1940s and 1950s.
Again perhaps not an obvious source, but it's often surprising what you can find in Flight!