I wonder whether the quote was for £1500 'plus disbursements' which could certainly push up the final bill. As already suggested, someone needs to contact the lawyers and request a detailed breakdown of the fees and disbursements to date.
As Carole says, if the estate is not particularly complicated, it is easy enough to obtain Letters of Administration without legal assistance. But obviously if matters are more complicated then to proceed without a proper legal representative would be a bit risky.
Regards
GS