I'd suggest a Discovery 300TDi too. They're good off road, and not to much of a compromise on road. They're also good to build up. However, they are prone to rust.
You will also find a Discovery II TD5 for a little bit more than that. (Or a few high mileage ones within your budget) But these are said to be less reliable than its predecessor. They are more fuel efficient though, quicker (afaik) and of course more modern. That said, if I was going to be doing serious stuff, I wouldn't want to be doing it in a newer Discovery II TD5 simply because there's a high chance it will get knocked about.
There's also the Freelander, but I suggest keeping away from the petrol model due to it being very prone to head gasket failure. The TD4 diesel model is also more fuel efficient than the Discos and Defenders, returning an average of 37mpg. They also deliver better on-road performance and comfort partly due to their monocoque chassis. However, the low ground clearance of the Freelander and the lack of a low range gearbox does limit its off-road capability. It's also worth pointing out that the Freelander is also prone to drivetrain issues and repair bills and can cost near £1000 to repair.
The Defender is ofc very good off road. Apparently they're not very suitable for long distance journeys. I do know that they retain their value very well. So with £4000, don't expect to buy one with many mod-cons. Other than that I don't know much about them myself because they don't really interest me.
So yeah, I'd say go with a Disco. (I stupidly bought a Freelander TD4 when I was making this decision a few months back) The Disco has the best of both worlds imo. Good enough for the daily commute, and capable off-road.