If you would like to seek gallery representation, the best way to make an approach is to send an email or letter with examples of your work. But please remember to keep you jpeg attachments small, under 1 mb is preferable. If the gallery likes your work, they will contact you to make an appointment to see your work properly. Galleries receive many portfolios every week and normally set aside a fixed time to review submissions. So please don't expect an immediate answer.
Never walk into a gallery with a portfolio without an appointment
The best way to annoy a gallery is to walk in and demand an immediate viewing, not only is this unprofessional, it can be seen as insulting as basically, you are suggesting the gallery has nothing better to do than look at your work.
If a gallery does accept your work and you are happy with the arrangement, please don’t then contact other nearby galleries for further representation. This is a very good way to upset a gallery. Every gallery likes to have a little exclusivity, and when you think that a good gallery will promote, advertise and generally work very hard for you, it’s not a good idea to jeopardize this. Having said that, galleries like to see that you are making a living from your work and that you have other galleries representing you around the UK. There are 86 counties in the UK, all with galleries!
Remember that you are working towards a good relationship with your gallery. To help communication, always keeps records of the works of art you hand over. Buy a notebook and ask the gallery to sign it after delivery. Try and make the gallery do the same if they don’t already. You could also suggest a three month trial period to protect both of you, so if after this period its not working for either of you, you can simply walk away.