Bit risky those timings. You definitely need to go landside since LGW only has INT-INT and DOM-INT flight connections. What we don't quite know is whether they are going to sharpen up the South domestic arrival experience, which is currently bus transfer only, whereas North can be airbridge (or bus). I saw some hints that suggested they were planning something in this area but I don't know how that shaped out. So if the ticket is flexible you could give it a go, but a Sensible Connection Time is going to be something like 90 minutes even with an on time arrival. Physically the minimum is about 45 minutes if via bus.