"How long will the grant of probate take to come through ?
Also, can anyone give me an estimate of the legal fees for what I would say is a straightforward case ? "
As the executor has appointed a solicitor, the query should be addressed to the solicitor.
The solicitor is obliged to provide an estimate or quote for fees before commencing the work. If they have not done so, the executor should ask for that now.
Equally, you could ring around a couple of local firms and ask what they would charge.
mf