There are mainly two types of closures - one is using sutures and the other is using staples. There are few clinics who use soley disolveable sutures - this technique you do not need to worry about getting them removed, but majority of doctors use the nylon sutures that need to be removed 7-14 days post op. Staples or nylon sutures both require separate types of instruments for removal.
The best places in the UK are probably the walk in clinics - I hear it's free for the service. In the US, a HT clinic, your general practicioner or walk in center. From my experience, there are different degrees of comfort level in who takes out the sutures or staples for each patient. I assist with many of our patients who want the reassurance of a HT clinic to take a look at the closure site and remove their sutures/staples. I call a HT clinic near the patient's homes. Majority of these clinics remove the sutures/staples for our paients as a courtesy service, therefore, there is no fee. Other patients are fine having any medical personnel take them out and I believe it's covered by their insurance. At a walk in center, I would suspect the fee may be around $50.
Taking out the staples is easier to learn (in my opinion) than sutures. But you do need to have the correct instruments for both. For sutures, you need a pair of suture scissors and basically a tweezer. For staples, you need a skin staple remover. Many clinics do not use staples so they may not have a remover at their clinic. We stock staple removers for our patients to take with them. Although, we rarely use staples at this time.