Starting my mortgage free journey which direction to take

Comeinpeace

Hi,

Im currently on a mortgage fix for 5 years at 2.59% on a 15 year mortgage in november ill be 2 years into my mortgage journey. I started with oweing £72000.  I have a bit of spare saving which i like to make the best use of my money what course of action would be best after the 5 year fix.  Should i wait until the fix is ended and then stick down a massive deposit when i come to remortgage while keeping my money in savings or should i start now and set up a money standing order paying monthly making overpayments on a regular basis.  With the current situation with everything going on at the moment possible house repairs,job security etc etc and saving rates being so poor some helpful advice on which path to take or suggestions would be appreciated   Thanks