No don't go near 26inch sprints, are you sure it is built for 26" wheels? It is possible it was built for 27" try some for clearence.Modern sprints(700c) should fit without mudguards. Or even Clinchers in 700c are still availlable in 32/40 drilling. Don’t get confused you are looking for 26x1 1/4 tyres not 26x1.25 they aren't the same.
Here is a good guide to differing wheel sizes
Are you after a period correct bike? Very expensive,especailly with a Hetchins which would have been kitted out with top end stuff.which is now 60 plus years old.
The wheels Chris has sound a bargain especially if it is an alloy shell Sturmey.
If you just want a bike you can ride it will be much easier and cheaper.
If you think the wheels are hard to find wait untill you start looking for a head clip.
Bakers Bikes in Bishops Stortford (Abel Baker Cycles Ltd 01279 658991 )
will be able to help with some bits, Join the VCC and get to one of the big cycle jumbles VERY early to beat the dealers.
Good luck with it and have a look here for inspiration
Before and after pics are always nice