Hi, Any bike shop should be able to dig around for the axle that fits. Few places sell 27" tires. Not a great selection anyways. But Freewheels,, the bearings(left & right) are closer together than newer,, Cassette rear hubs. So freewheel axles break easier.
But swapping 27 for a 700C Wheelset. You have to lower your brake pads. If you can put the bike back together for not much more than the axle replacement, I'd do it. cheers,//