Trademarking a logo isn’t essential, and I would wager that most businesses don’t even bother. It does however add some value to the imagery (and potentially words) that you have come up with, and it is something that would become vital as you look to grow.
Registering a trademark is relatively simple, and you can either do it yourself through the IPO (Intellectual Property Office), or through a trademark attorney. Typically a trademark would cost you approximately £200 if registered yourself, or £500-£600 if you engage a professional to do it. There are different fees based on how many classes (types of business) you would like to register the mark for, and the whole process takes some time as the IPO have to check that there are no competing marks, and also that the registration is publicised should there be any objections.
Provided that the trademark fulfils the criteria set by the IPO – in that it is distinctive, that it’s not descriptive, not offensive, not deceptive, and not customary for your industry, the process should be relatively pain free. If however there is a dispute over the eligibility of a mark, it is worth seeking professional advice and weighing up whether it is worth proceeding with registration. I’ve personally registered marks myself and via professionals, and the attorneys know how to present a case in the event of a dispute, which I would not have otherwise been able to put forwards.
You would also need to consider whether you wish to register just a logo or words, and also whether you would like to register for just the UK or also overseas.