Can I claim my mobile phone on expenses?

I have been self employed since I had my first child a few years ago. I file a self assessment tax return each year. My job is heavily focused on online work. My query relates to allowable expenses. My current mobile phone operates well, but is quite old and therefore I’m unable to download many apps etc that I require for work purposes. I understand I can claim a proportion of my ongoing phone costs, but can I claim the full (one-off) cost of a new phone as a business expense? It will be used for both personal and work purposes, but I wouldn’t be replacing it for a more up-to-date model if it wasn’t for the fact my job requires it.