A solicitor will normally charge five quid for witnessing a document although it depends what it is, sometimes they will charge 20.
A notary on the other hand will want an arm and a leg and to both kidneys and GBP55 is cheap for the notaries signature. The only reason for using the notary is for documents which are going to be used internationally. Otherwise forget it. The notary or solicitor will want paying instantly.
You can search the Law Society website www.lawsociety.org.uk
By postcode to find one near to you. The only reason you may have a problem is because there is actually nobody in the office.
It’s a case of making the loader telephone calls.
I don’t know what the document is but very few documents other than statutory declarations, affidavits, and certain mortgage deeds, need witnessing by a solicitor although if you are making an application to the land registry they would want the photograph on form ID1 certified by a solicitor for which the solicitor will charge whatever they like because if you are DIY you are taking work from the solicitor.
Depending on what the document is and what it is for, the recipient may be happy to take remote witnessing via video link. Unfortunately it’s not satisfactory for court documents.
If you can find a court office open, the court staff can witness it for you and that would be acceptable by 99.9% of places.