Hi, just a (biased) input from someone who runs a PPC management agency. Hopefully this helps you out!
First, it will be difficult to find a company who will manage a budget of £250. Since we usually charge 10-15% as one poster said above, that's only £37.50 per month. Most of our clients have $5k to $30k monthly budgets, so those make more sense for companies to focus on. We usually don't even take clients who spend less than $1000/mo.
I would suggest digging into some resources and learning how to do it yourself: there is a lot going on behind the scenes and it can be hard to get a good grasp on strategy especially if you don't want to "experiment" with your own money.
One of the most important things to remember to keep your spend efficient is: don't take what Google's recommendations are too seriously, since they want you to spend more on their platform. Also, if you do grow to the point you need someone else to manage or consult, look for a company that has shown proven results and isn't trying to get you to spend more $$$ without significant ROI.
Hope that helps!