Some advice :

Malaga - Barcelona : as you seem to live in Spain, go to a RENFE ticket counter (10€).

Barcelona - Montpellier : 2-3 options

1. Direct TGV : 27€, very popular so book well in advance

2. Direct AVE by RENFE (line restarting on 13th July) : not known yet whether they accept passes.

3. Fully reservation-free by taking the coastal route via Portbou :)

TGVs within France : limited 10€ fare, then 20€.

Montpellier - Lyon could be done reservation-free via Avignon using TER regional trains but there are direct TGVs too. Be aware that there are 2 stations : Montpellier St-Roch (in the center) and Montpellier Sud de France (outside the city).

Lyon - Paris - London : actually I'd recommend going via Lille as it avoids the RER transfer between stations (not included). Unless you want to make a break in Paris ofc !

Paris or Lille - London : 30€ seat reservation. There is a quota for passholders so you need to book ASAP.

London - Edinburgh : optional reservation (but recommended). Free of charge through LNER.

For this journey a 5-day Global Pass should be enough but if you're planning day trips from Edinburgh or elsewhere in the UK, I very much recommend the 7 or 10 day pass as British train tickets are very expensive.