Oh another PPRuNe example of the facts not being allowed to stand in the way of hyperbole.
Swear fees are set by the rules under which solicitors practise so the fee will be the same whichever solicitor you go to. £5 for the affidavit and £2 per exhibit.
Any solicitor holding a current practising certificate can administer an oath as can some duly authorized court officers so if you live just round the corner from your local county court you could try there first.
I would be pleased to assist but am based in Yorkshire. Don't worry about whether the solicitor even knows what a log book is - they probably won't even be interested in the content of the affidavit. The significance is the swearing as to the truth of the contents and the signing of the affidavit before them not the content of the affidavit.
Suggest you try any high street firm because you are more likely to be able to see someone straight away without an appointment. Talk nicely to the receptionist and they will probably find some hard up newly qualified solicitor who will be grateful for the cash and only too pleased to assist.