The only reasonable case for conversion is as part of renewals, and that's because it can cost as much to renew the DC infrastructure as to replace it with new AC kit, with the advantage that you could install much of the AC kit alongside the DC, so ignoring it in favour of unelectrified lines doesn't really make sense, as the already-electrified lines are llikely to be those most intensely used already, so being able to increase their capacity by enabling more frequent, and longer, and faster trains than the DC can supply (due to greater current being available) is going to give greater benefits than switching over a more lightly-used diesel line elsewhere to AC.
Primary obstacles that increase costs are a) signalling - i.e. is it suitable for use with AC, and are the signals themselves in suitable locations once the masts go up? b) ...and tunnels (including the very short tunnels we call bridges
). The signalling issue can be dealt with as part of renewals of that separately (are all new signalling installations suitable for use with AC now?), and tunnels are usually dealt with as part of gauge enhancement improvements for freight. Where there isn't any notable containerised freight then it becomes more problematic.
As an additional consideration, when it comes to working out how to switch over viable routes you recover DC assets from lines suitable for conversion that aren't life expired and use them to renew those in problematic areas that aren't. Eventually the DC network contracts back to the inevitable core of the central London area and you just need one almighty push to finish it off, everything being dual-voltage these days really helps here. Just gotta get those extremities of the network switching over...