Yes you can remortgage and use some of the equity as a deposit to make your next buy to let purchase. This is a common strategy used by property investors to grow their portfolios.
If you take this route, the lender will instruct a valuer to formally establish the present value of your existing property which will determine exactly how much equity you have to play with. You will have to pay for this valuation.
Alternatively you could ask your current lender for a further advance on your existing mortgage. Again, the lender will require that your property is formally re-valued.
Talk to a specialist buy to let broker who will be able to help you work out which route makes the most financial sense.