Looking in some of my favourite books from time to time recently I happened to read a little bit deeeper into BRP stories, which leave to me the impression, that somehow they seem to have been like a black sheep. And this not only because they were not allowed membership in the F1CA, but already before. Now reading this thread seems to confirm my suspicion, that there must have been something, without finding some really satisfying explanation for this 'something'. As the discussions are some years old maybe in the meantime somebody could have got some newer insights?
To elaborate about this, a brief recapitulation of the team´s history. To my understanding it was founded by Ken Gregory and Alfred Moss around 1957 as kind of a 'backup' for Stirling Moss for occasions when he did not have a works entry somewhere. Besides that it was run mainly as a Formula 2 team until 1959. In 1960 with Yeoman sponsorship they progressed into a full-season 'customer' Formula 1 team with Coopers. Interestingly Stirling Moss preferred to carry on with Walker, but BRP/Yeoman were present at every Grand Prix besides Argentina (probably because of the distance) and Italy, where there was the boycott of all the British teams. Noteably BRP were present at Zandvoort (and with three entries!), while the German GP was for Formula 2 that year. The reason for my last remarks is, because in the following years BRP seem to have got problems in particular with the organizers of these two events. The Dutch seem to have been notorious to accept only entries they had explicitely 'invited', while the Germans seem to have had no comprehensive policy at all, admitting real no-hopers sometimes and refusing well-established teams and drivers on other occasions. The Belgians and French seem to have been similar reluctant in their policiies, but it seems they did not have objections against BRP.
Ok, so as written above, in 1960 BRP seems to have been treated very much as a quite normal 'private' team, but in 1961 (now renamed as UDT-Laystall) they were neither running at Zandvoort nor at the Nürburgring, One could assume, that the Dutch organizers would have maybe only invited 'manufacturers' (as had been quite a tradition in Grand Prix before), but in contradiction to that they accepted or even invited entries for the Parnell team (this year under Yeoman Credit sponsorship). And they even had two Camoradi entries as 'reserve'. And in Germany there were even a lot of pure 'privateer' entries (in the sense of owner/driver) like Ashmore, Marsh or Lewis.
In 1962 BRP was actually present at Zandvoort, but for the German GP in my records I have explicitely noted "entry refused" for Ireland and Gregory. Again, there were much less attractive entries (Lewis, Burgess, Shelly, Chamberlain even Collomb), so that is really asking for a background story!
In 1963 problems seem to have been settled, for BRP ran two entries throughout the season before Ireland got injured for the races in America. But then comes 1964 and BRP is absent again at Zandvoort and the Nürburgring, And I can absolutely see not any reason why somebody would turn down BRP, (at least a 'semi-constructor' and with a former Grand Prix winner as driver) and instead allow somebody like Bob Anderson to drive.