It will be dependant on whether you have a deposit or not.
If you have a deposit then you can put this down and get a mortgage for the property. If you do not then no lender (yet) gives 100% mortgages and so you would not be able to buy the house. No lender will allow you to use the equity you have in the existing house towards the deposit but you could get a new mortgage (without any penalty) to raise the deposit from your equity and to pay for the deposit on your new house.
If you have the deposit then you can apply for the new mortgage on the new house but this will be subject to affordability on both houses as you will then have 2 mortgages and there is no guarantee that your current house will sell tomorrow or even in the next 5 years so you have to be assessed on both houses. To offset this you could look at renting the existing house as this would then mean the full mortgage is paid by rental and will not be counted towards your affordability costs but you would need to obtain what is called consent to lease from your own lender before you do this and the new lender will most likely look for this if you are declaring rental for the existing house to help with affordability.
Your best bet is to go and speak to a mortgage broker and he can advise and guide you through this whole process easily.