25kV conversion in the southeast and indeed of Merseyrail will be a significantly easier project than electrification of non electrified routes, though there will be some big engineering projects in the fullness of time
The big cost will generally be bridge replacement and track lowering works, but that's running really rather beautifully at the moment across all the various electrification projects. There will also be tunnel reboring needed, but many of those structures are getting towards the end of their lives in any case and rebuilding for 25kV clearance won't cost any extra, indeed, with equipment like Fillie available, 25kV clearance will be the cheaper option.
Network Rail have a pretty damn good contractor in Murphy and their sub-contractors, like Shay Murtaugh and Buckingham. These guys have really improved in the last few years and they're quick, safe, reliable and get things done on time and on budget, with minimum fuss. The utilities like BT, United Utilities, National Grid, Scottish and Southern and so on, they're now more aware of what needs to be done when a bridge is removed and replaced, and they now have the skills and understanding to get all their wires and pipes off the old bridge, out of the way, first time.
The S&T people in third rail land know electrification and things like EM interference inside out and back to front, 750V DC is noisy, dirty electricity and isn't kind to S&T kit and it isn't kind to traction kit, as a result, everything that needs to be in third rail land is screened cable and EM hardened, yes, some immunisation works will be needed but it'll be done by teams that have worked on an electrified railway previously and just have that extra little bit of hard won experience, keeping their signalling running in places like Clapham Jn.
The southern S&T people tend to be a damn site more disciplined with their signalling cabling runs too - none of this silly buried and forgotten about cabling that Western managed round Reading, which did so much to put the GWML electrification behind schedule.
The good thing about converting the Southern is it's electrified already, dual voltage stock is in common use - so conversion can be a relatively slow process dictated by the replacement of the life expired 750V DC equipment - you can install the actual overhead catenary at a fairly constant pace to keep the engineering teams fully utilised, but choose to energise and make the switch when it suits the TOCs. You could be installing 150 track miles a year but choosing only to use 100 miles one year and 200 miles the next year.