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I think Condor at one point made a fixed gear frameset with horizontal dropouts precisely for this reason
This sounds interesting, but I really don't quite understand how this was supposed to work.
For what it's worth, I have tried removing the back wheel from my Gillott (see post 2980 above) and it's tight, but it can just be done without delating the tyre. It's perhaps worth noting that this frame is now quite a way from the builder's original intentions, since it now has Campag ends and 700 wheels (probably intended for 26" since it dates from about 1950)
clubman-
Turns out they still make it - it's called the Tempo. There's a photo on their website of the dropouts and the set up with mudguards https://www.condorcycles.com/products/condor-tempo-frameset?variant=45755739504961
Momentum
I think Condor at one point made a fixed gear frameset with horizontal dropouts precisely for this reason, as the frame was designed for commuting/audax with mudguards. I had a Surly crosscheck set up fixed like this and it worked well.
As @hollow__legs says you end up with a gap at the front of the mudguard which doesn't look great. Velo Orange make a spring loaded nut and bolt to help - it holds the mudguard close to the tyre and then you can push against the spring if you need to remove the wheel https://velo-orange.com/products/spring-thing?srsltid=AfmBOoqZPrGmxj8zFrNDAFMahqMMoeH5FiIpwL2FKOM43NBh8PJqVQup