The four shops I know of that have a decent selection of ukuleles in the UK are Duke of Uke in London. Southern Ukulele Store in Bournmouth, Eagle Music in Huddersfield and Omega Music near Brampton in Cumbria. Some say Windows in Newcastle is OK. Last time I was in York, Banks had an OKish selection. There may be others but these are the ones I know of.
I bought a melodeon from Eagle music several years ago and I've bought stuff on line from them and always found them very helpful. Eagle music set their instruments up so I would definitely recommend them.
As an aside, it's a good idea to put your general location in your profile so it shows on your posts. It helps when you make queries like this.