A Global Pass is valid all the way but you'll need to add seat reservations on high-speed trains. This will be a significant part of the budget : Barcelona - Paris TGV 35€, Eurostar 30€. Have a look at https://www.seat61.com/interrail-and-eurail-reservations.htm
There are no night trains in Spain but some leave from the Spanish border towards Paris -> Latour (Pyrénées), Cerbère (Mediterranean) would be convenient to you. Around 20€ for a couchette.
London - Barcelona is one of the most expensive routes possible I'm afraid... A pass is still likely to be the best choice as advance tickets are very expensive too.
There are a few ways to save money but not many : for example reservation-free regional trains on Barcelona - Cerbère - Montpellier before a northbound TGV. Also possible to take a Montpellier - Lille TGV to avoid the station transfer in Paris.
I'd recommend the daily Barcelona - Lyon AVE : only 10€ vs 35€ for the TGV. Reservations are only available at Spanish counters but if you live in Barcelona it shouldn't be an issue. Probably the best option to cross the border!
For timetables you can have a look at DB Navigator app. Do note that most summer timetables have not been published yet.
EDIT : You need to calculate how many pass days you might need. I guess 7 days in a month or 10 days in 2 months could be the way to go.
British train tickets are fairly expensive last-minute so using an Interrail pass day is a good choice for flexibility. Reservations are always optional and free of charge.
Feel free to ask further questions, we'll gladly help. :)