Much more likely than an E-Type special in my opinion. e.g. it's got the D-type/Lister wheels and I doubt the special-builders were using E-types as raw materials as early as 1964.
The photo caption may be based on the race day programme and car 1A may have been something quite different as a late substitute.
There were other "flat iron" Listers of course and the Border Reivers car didn't have the rear air scoops at Le Mans when they'd be necessary if ever they were.
Indeed - as Duchy says, it's definitely the ex-Border Reivers car HCH 736, although at this stage is appears to have had the number plate removed and the rear brake cooling scoops fitted. To be fair, in the days before "modern" high boiling point brake fluids, the inboard rear brakes were notoriously prone to overheating on Listers and pretty much everyone from the works, to Ecosse, to journeyman privateers fitted scoops of some description in an effort to get cool air to the diff./ caliper area.
At the time, the car was owned by the Hon. Richard Wrottesley, and I believe the curious quartered flag colours on the door (and, if my eyesight doesn't deceive me) the driver's crash helmet were the old family horse racing colours. I believe he was what is known as a "colourful" character, and my father raced against him extensively in the early 1960s in Formule Libre events. HCH had, by this stage, started to look very second hand which - from my mother's first hand recollections - could apparently also be said of Wrottesley and his entourage....