A No. 7 receiver - or a No. 4 receiver, for that matter - could be used to build up a .22. Unfortunately, the receiver is the easiest piece to locate.
Bolt heads do turn up, or a .303 bolthead can be altered. Bolt body is the same. The chances of finding a barrel are slim. A .303 barrel can be altered. It has to be extended to the rear and sleeved.
Getting a complete rear sight will take some looking.
Basically, assembling a No. 7 from parts is going to be an uphill struggle.
Assembling a .22/.303 conversion is possible, basically a homemade equivalent of a British No. 9 rifle.