^^ Yep! Another way to ensure tight fit to bolt face is to create a "false shoulder" - in effect, cause that round to stop forward movement with its shoulder - only works when the round is being reloaded, though - This procedure probably does not work with factory ammo - if previously fired brass, that "stretch" may already have occurred - works with any shouldered and rimmed or belted case - about same issue - although military 303 British often had their chambers enlarged over standard, which was commonly NOT done with other rimmed cases like 30-30 Win or with most belted cartridges.
For OP - many 303 British headspace gauges look like a washer - they will only measure the "headspace" dimension from the bolt face to whatever stops the forward edge of the rim - usually the rear end of the barrel or a slot cut in there. Canada and Australia "relaxed" their headspace requirements during WWII - so be careful what you end up with - a military FIELD gauge from early WWII is a couple thousandths shorter than a military FIELD gauge from near war end. Most commercial vendors now sell a SAAMI spec'd gauge - not military, but many will still use a military gauge - even though the factory ammo sold in North America is probably made to SAAMI spec - there is probably some merit to using SAAMI compliant gauges and SAAMI compliant ammo. As a bizarre example, I found - SAAMI spec'd headspace is MUCH shorter for Swedish 6.5x55 - typically the SAAMI Field gauge for 6.5x55 is shorter than the Swede Regimental "GO" gauge used at their arsenal - I do not know why SAAMI did that - certainly the Swedes were making and using 6.5x55 long before (decades before) SAAMI existed in USA. I read that an Armourer in the field only used a FIELD headspace gauge - if the bolt closed on that, then the rifle was condemned and replaced - that rifle had "too long" headspace to be safe to fire - it needed it's barrel set back and re-chambered if the bolt lugs were still holding - was done at a base or something, not in the "field". The rifle accepted standard military ammo, so that chamber was at least GO gauge length - no need to check for that. A "normal" headspace gauge will not measure a 303 British case body dimension - not length or diameter - it's "head space" criteria is only from the closed bolt face to a specific spot within the chamber - it only measures to whatever is supposed to stop the cartridge from going forward from that point. Results in much confusion about headspace - so 30-06, 308 Win (7.62x51) and 223 Rem (5.56 Nato) are different than 303 British
So run the empty case into a a die with larger Neck Expander - for example, run 303 British into 338 Win Mag or larger - run 338 Win Mag into 375 H&H - idea is to create a grossly oversized neck diameter. That might take some steps - first to .30 Cal, then to 8mm Cal. then to .338 Cal, then to .35 Cal, etc. Then start with correct sizing die, set much too high - perhaps re-sizing only half of the case neck - that will create a goofy looking resized case with a "false shoulder" - try that in your rifle - the bolt will probably not close. Slowly turn the sizing die down in the press - try each time in the rifle - sooner or later you will find the few degrees of turn of the sizing die where the bolt will close when die turned in and will not close when die turned out - you are very close to "tight" between chamber shoulder and bolt face. So your sized brass fits to your chamber, now. Nothing says what you did will fit to anyone else's chamber though, but it snuggly fits yours. Nothing says that your chamber is still to a SAAMI spec, but that brass is fitted to that chamber, now. Sometimes you still have a goofy looking "false shoulder" - first or second firing will "blow that out" to match the chamber - re-size as needed to just barely re-chamber.
A "down and dirty" way to "check" headspace on your rifle - computer printer paper is .004" thick (or thereabouts) - how many circles/ layers of paper fit between the closed bolt and cartridge head?? - that is the "headspace" of that cartridge case in that chamber, with that bolt. The case is as far forward as it can go - against the "headspace point" - the bolt face is as far back as it can go - held by its lugs or seats - the "gap" between the bolt face and the cartridge case is taken up with the layers of paper. Look up SAAMI Standards - GO to FIELD (Min to MAX) "headspace" is often shown as 0.007" difference for 303 British - not the same difference for all cartridges - I think 30-06 is like 0.010" difference - so if you have 2 layers of computer paper, you are probably about 0.008" gap - likely you are close to or over FIELD (Maximum) headspace. I had read of others doing similar with masking tape stuck to cartridge case head, but I do not know the thickness of their tape - I never tried that to measure it. The main issue I see is that you have no way of knowing where GO is (Minimum) - all you will know is how far apart the bolt face and case face might get. Sometimes a protruding primer will tell you the same - but that means you have to fire the rifle first, with a known full power load - not a "reduced" load.