If you sell your property then you will be required to redeem the mortgage in full. The lender is hardly going to lend you money against a property that you no longer own.
It is also illegal to have a residential mortgage on more than 1 property. A residential mortgage can only be placed against your "Main Residence" and if you have moved then the old property is no longer your main residence and therefore the mortgage would not be viable anymore, this would only apply if you were not selling the property though, as stated before, the lender would want the mortgage fully resolved if you were moving to a new home
As you want to continue with the current reserve account on the mortgage then I would suggest that you speak to your lender about "porting" your mortgage. This is where you will transfer your existing mortgage over from your existing property to another property once you have sold your existing property. Effectively the new property will carry the £10k mortgage from the old property and under the same mortgage account but a new side loan you would then arrange to borrow anything additional you would need to buy the house.
This would mean you keep the benefit of the reserve account and can just set up a new product to buy the new house.
You may even find that if you fully redeem your existing mortgage (when your house sells) and just take out a brand new mortgage product that you can either get a similar reserve account with another lender (plenty of them will do something similar, speak to a mortgage broker for details) or that your existing lender can offer you something more attractive for the new property
Best option for this is to call your lender and ask about "porting" your existing mortgage or speak to a mortgage broker and see if he can suggest any similar options.