I have banked with most of the big UK banks Barclays, RBS, Lloyds and HSBC.
The one I would recommend for service and speed is HSBC. All of the above will provide free banking, online access and credit cards. However I found HSBC the best when it comes to customer service and speed of transfers.
With regard to moving your £10K, the exchange rate is set by the sending bank. Most banks won't give you their corporate rate unless you are moving more than £25K and you need to go into a branch in order for them to lock the rate with their Group Treasury department.