You can book everything via Interrail but you'll pay extra: 2€ booking fee per person and train and 9€ postage fee per order for reservations that are only available on paper.
Barcelona to Lyon and Lyon to Barcelona: this reservation is only available on paper. Since you're from Spain, thee best is to buy these reservations from the RENFE ticket office. It saves the Interrail booking and postages fees.
Brussels to London and London to Paris: You could also ask at the RENFE ticket office but I'm not very hopeful. Other options (all will send the reservations by email):
hello,
I have tried to do it through interrail but when the last step arrives it does not let me click on pay.
I want to do it through interrail to do it all at once and together. We want to have it all planned and paid for before we leave.
thank you very much again
You can do it via Interrail but it will cost more because of all the extra charges. And they seem to have a problem with the reservation service today.
The other options I mentioned can certainly also be used to book in advance.