Unfortunately, this sentence is a contradiction. ‘Porting a mortgage over’ still means you are getting a mortgage.
All you are doing is keeping the same financial deal (i.e. the interest rate/product) for the mortgage over your new houses as you have on you current one. Your lender will still require a valuation of the new property, they will still need to decide if it is a house they will lend on, and they may still only lend you a certain % of the purchase price. Your application to port may prove unsuccessful as a result of any of these actions.
But it may mean less administration by your existing mortgage provider and so your conveyancing solicitor could receive a mortgage offer more quickly.
Your conveyancing solicitor will still be involved in repaying your current mortgage from your sale proceeds only to then receive a fresh mortgage advance from your lender to secure the new mortgage on the new property.