The best places to buy genuine accurately graded coins is always from decent dealers (online or at coin fairs) and dedicated coin auctions (of which there are several), such as DNW and London Coin Auctions.
For your needs right now it may be best dipping your toe in to the waters of a few dealer web sites, such as that owned by this forums's owner (Chris Perkins - http://www.predecimal.com/), Colin Cooke, R.P Coins (Rob on here), http://www.pennycrowncoins.co.uk/ (Derek - Red Riley on here), and others.
Depending on your storage / presentation needs it does sound like a 1951 set might fit the bill, should cost around £100 for a decent one, this is the set I am referring to:
http://www.ebid.net/uk/for-sale/1951-gb-specimen-proof-coin-set-festival-of-britain-royal-mint-129816182.htm?from=googleshop_uk&adwords=Y&gclid=Cj0KEQjwwYK8BRC0ta6LhOPC0v0BEiQApv6jYb5Cd86nHOITGj6k1582NbsFbYqdl52INNs8Xd3QY7gaAsJd8P8HAQ
The penny in that set is relatively scarce
Edit: But I wouldn't buy that particular example