If you want to be cautious no more than £75k in any one bank. Do not be duped into ISAs or other savings products. Look at 6-9 month term deposits (note you cannot withdraw early without penalty).
Short term,up to 6 months or so, these protected limits are increased significantly, recognising that ornery folk will occasionally have all their dosh in one account.
http://www.fscs.org.uk/news/2015/july/new-protection-from-today-for-temporary-high-balances/
As Jamba says, ignore cash ISAs. Their rates are pitiful.
Santander 123 £60k (one a/c each and a joint) at3%, Lloyds club £5k each at 4%. Other higher interest a/cs are available but for pissy little amounts. Al Rayan bank has some of the best interest rates available, 1.5% on a 120 day notice a/c.
As said though, premium bonds are worth a punt and NS&I accounts are the safest you can get bar none!
You can pull your money out of PBs and NS&I a/cs instantly; instant meaning a couple of days…