Sorry to disagree but an LIP CAN claim for their own time - Civil Procedure Rules 46.5(3) states that they can claim for the same categories of work as would have been allowed if the work had been done by a legal representative. Rule 46.5(4)(a) states that, where the LIP can prove financial loss, they can claim the amount they can prove they have lost for time reasonably spent doing the work. Rule 46.5(4)(b) states that, where the LIP cannot prove financial loss, they can claim at the rate set in Practice Direction 46 (currently £19 per hour).
I just want to emphasise that the normal order in financial proceedings is no order for costs - ie each bears their own. You need to prove special circumstances to get a costs order from the other person.
MrsBB posted the link above, to FPR Part 28 rule 28.3(5)
if the intervenor is a party to the full financial proceedings, you might encounter an argument that 'the normal rule applies' ie no order for costs. But in my experience, the court will accept that the only purpose for the intervenor being involved is to determine the beneficial interest. So if you win on that point, you win, and costs should "follow the event" ie be paid by loser to winner.
It is helpful that it is a separate hearing, not mingled in with the full financial hearing.