Whilst 25-pounder batteries did receive a small number of anti-tank shells as a just in case measure it probably wouldn't have been a good idea as a dedicated tank gun. The main problem that I can see is its much lower muzzle velocity in comparison to the anti-tank gun, higher velocity generally means the shell traveling a longer distance in a flatter trajectory, making it easier to hit targets, as opposed to the artillery shells more curved one.
Edit: Missed RLBH's post.
The anti tank round used the charge super increment, and the guns were altered to have a muzzle break for use of that charge. (The early model 25 pdr have no brake).
The problem with the 25 pounder as a tank round is that it's a howitzer, with separate loading (round and brass case containing the charge). The case came with max charge (not super) loaded, and the detachment fished out any unwanted cordite bags as needed for the mission. Charge super came separately, and was plonked on top of the felt liner that sat on top of the charges.
It had a very fast rate of fire, even us army cadets got the hang of it fairly quickly on our course at Larkhill camp back in the early 1970s. However, that required room for the loader to operate alongside operating his wooden "plunger" to first shove the round up the spout, and the second loader/ammo number to then throw in the brass. It also required the loader to manually trip the breech just before the rearmost of the recoil so the brass was thrown out by the rearwards motion of the barrel.
Post our live shoot, all the unused cordite bags were put in a pile on some chalky ground, and set off with a flare. Quite impressive!.
None of that would be possible in the confines of an enclosed turret. Nor does it seem to have been the case with the SP Bishop(?) - which seems to have been loaded by a guy kneeling on the back deck, with the rear of the mount open (it was not a turret). So Bishop probably had a fairly modest ROF, as well as being limited in maximum range due to the mount's low elevation.
For a tank gun based on it, you would need a single piece round with the brass crimped on. Not impossible to do. However even with charge super, it was not a particularly high velocity weapon. Therefore its use in the A/T role in the desert was in extremis only.
A HESH round was developed for it post war.
All in all - the 25pdr is probably not a valid path to go down, if looking for a tank killing gun. In addition, it was only just coming into service at the start of the war - 18 pounders were still in service, and there was a hybrid 18/25 pounder mount using the older gun chassis. So its a priority item for rearming the field artillery and unlikely to be diverted to tanks.
It would probably have been better for an inter-war tank design to use the good old 18 pounder as its gun since it is going out of service. That is about the same sort of gun as the US 75mm, which was just a version of the French 75 field gun of WW1. Against early war tanks, it would do the trick perfectly well. So design a tank that uses the 18 pounder, and use barrels that were still in adequate condition. It throws a decent HE round, and would have adequate A/T characteristics - the US 75 served through WW2 after all, only being regarded as lacking in AP poke in about '44 onwards. It would tide you over whilst the 17 pounder and 77mm are being developed. And if you had an 18 pounder tank gun, you may not see the need of the 6 pounder as a tank gun (still useful as an infantry ATG though).
