Not that I measure end shake on much of anything besides S&W revolvers, but on these the cylinder float can be controlled by adding "O" shaped shims between the end of the yoke ("crane" to Colt types) and the cylinder ID. I will often set it to 0.002" on general purpose Smiths and 0.001" on hunting and target S&Ws if everything else is running true. I run many of these revolvers fast and dirty. No dramas to date. My old 686 .357 has had multi tens of thousands of rounds through it. End shake is still tight, but that's about the only thing!
The usual binding drama on Smiths is when the cylinder drags against the rear face of the barrel, which the shims will cure straight away.
As for the Enfield revolver, it never occurred to me that the forward motion of the Enfield's cylinder would be controlled by anything other than cylinder axis' rear face (which shimming would change, if so.) or the front of the cylinder sleeve which is very "beefy". But I've never had a binding drama with one, nor headspace so excessive that misfires occurred. So it's been of no concern until now! Given the low pressure of the round, binding due to cartridge set-back seems highly unlikely.