965x500mm is a pretty standard size for a stainless steel sink but 1000mm is not that uncommon either.
Is yours a 1 bowl or a 1 1/2 bowl sink? Size makes me think it is probably a 1 1/2 bowl?
Granite composite sinks tend to be larger than their stainless steel counterparts and ceramics will tend to be slightly smaller.
Most decent manufacturers will supply their sinks with all the required bits and bobs. You will need sealing tape for round the edge of the sink and clips to secure it to the underside of the worktops. The sinks should come with any wastes required but you may need some extra plumbing bits for the underneath. Your plumber should be able to sort you with that but places like homebase/b&q will also sell these.
When buying your sink think about what side the drainer is going to be on. Most sinks are reversible so will have a tap hole drilled in both sides with a cover cap allowing you to blank off the one not used. However some of the more expensive sinks will be sold in Righ Hand or Left Hand versions. If you go for a ceramic or granite composite sink these usually have tap holes pre bored on the underside on both sides which are tapped out depending on which way the sink will be orientated so are reversible.
Have a look at Carron Pheonix sinks for decent quality and i think a 50 year guarantee. They do have a number of sinks which will fit your needs.
Another manufacturer you might want to loo at is Franke. Higher quality than the Carrons but you do pay for it. Their sinks tend to be a bit larger so might be worth a look.
I assume you dont want to replace the worktops you currently have? If so you will need to find one which has same dimensions or is slightly bigger. 1030x510 next size up.
Something like
http://www.carron.com/products/sinks/stainless/****/276_ai2150il4kca
or
http://www.carron.com/products/sinks/stainless/cuba/281_cuba-150
or
http://www.carron.com/products/sinks/granite/java/244_java150-sg
or
http://www.carron.com/products/sinks/granite/zx/9_zx150-gg
or
http://www.frankekitchensinks.co.uk/index.asp?SKSID=840&ItemID=3373
or
http://www.frankekitchensinks.co.uk/index.asp?SKSID=840&ItemID=2051
Whatever you do dont let your plumber sort you out with a cheap no name sink. Most of these use steel so thin you can almost see through them!
I know homebase sell both carron and franke sinks if you want to see the finish/quality before you buy. Be aware though their lead time is around 4-6 weeks for a simple sink.
Hope this helps!