Yes, spread between 2 institutions- although personally I think that if ever a major bank went bust and the protection arrangements had to be used then all the banks would follow and the economy would collapse anyway.
If you pay tax (on earnings, pension + savings) you should maximise your ISA allowance too.
I'm not sure about premium bonds- is there still a waiting period of a few months before you are eligible for prizes? VHG may need the money before he wins any prizes