BSA tank badge looks like a one-off, and the tank itself appears to have been sourced from some later bike. Certainly the seat and front fender are replacements, and the oil cooler is an add-on. But frame and separately lubricated crankcase and twin-cylinder overhead-valve engine confirm this as a BSA is from the pre-unit era. I'm thinking it's a 650 A10, as built by the famous British manufacturer between 1950 and 1962.
Another representative of the golden age of British motorcycles was this much-festooned Triumph. Underneath all the fringes and stickers, it looked largely original. I feel fairly safe in calling it a late-1950s T110 Tiger 650, but I'm sure someone will correct me if I'm wrong.