It's a perfectly feasible journey, but it will cost you quite a bit doing it at those times and on those specific trains.
You'll probably want to buy something like:
- Neath-Cardiff Off-Peak Day Return (CDR) - £10
- Cardiff-Newport CDR - £4.90
- Newport-Cwmbran Anytime Day Single (SDS) - £5
- Cwmbran-Birmingham Anytime Single (SOS) - £25
- Birmingham-Derby Off-Peak Single (SVS) - £19.20
- Derby-Reading Super Off-Peak Single (SSS) via London - £86.20
- Reading-Didcot Off-Peak Day Single (CDS) - £6.90
- Didcot-Newport SSS - £33.90
Which would be a total of £191.10.
It may also be possible to do some of the legs cheaper using Advances, but I've just searched for walk-up tickets there. I also haven't looked into which leg would be cheapest/best to do in First.
The reason why it's so expensive is that you are effectively making two one-way journeys (as there isn't any through fares valid from Neath/Newport to Derby via Hereford as well as via London) - and walk-up single fares are often priced at just £1 or so less than the return.
If you altered your journey slightly so that you made your route something that could be done with one ticket - for example if you went via Nuneaton and Leicester rather than via Derby - it would be considerably cheaper.
You could then buy something like a Neath to Kettering return, buying the cheaper via Newport route for your outward journey (£95.30) and excessing it to via London for your return journey (which would be half the difference, so £12.25 if you took a train departing Paddington after 19:00, or £40.05 for one departing after 18:30). Total cost would reduce to £107.55 or £135.35.
Theoretically the via Newport fare is also valid via London (as it isn't "not via London" for example), but you can be sure it wouldn't be accepted on the Underground as it lacks a Maltese cross, and there is also the possibility of problems using it via London on the trains. Probably best avoided, for the sake of a £12.25 excess.