V v difficult.Do these customers know that you were just starting out at the beginning?

I think you do need to increase the prices. It may well be that you don't increase to the full maximum price, but nonetheless it has to go up. You should be prepared to lose customers as I suspect one of the reasons they love the service is they are getting a gold-level product at a bronze price. But, assuming you're doing quite well, I imagine that you would be able to replace them. The really important thing to keep in mind is that if they are causing you to lose money, no matter how bad you feel, you can't continue to service them.

So a note sent via text message or email or whatever saying, "Thank you for your loyal custom. As you can imagine, costs etc continue to rise and as such it is necessary to increase my prices in line with the market to xx".

As a side bar and it's too late for you really but someone told me when I was starting out to be very very careful of accepting work at very low prices just because it's work. For this exact reason. It's hard not to, but you have to accept the reality that it does mean that at some point you may have to jettison those clients.

I'd just start increasing their prices at a faster rate than the new customers. Send a blast text/email/letter around all older customers to say that as of 1 April, prices will be rising by X. Maybe 5%? Then do the same October. Then April etc. Until they come closer in line with newer customers.

If you are charging new customers £X then the market can support that. There is no point in getting out of bed and going to work and not making any profit. I would give a decent notice period and then bring the old clients in line with the new. Some people will reevaluate whether they want to pay for your service at all, and some whether they want to pay at the new rate but it is unlikely that you will lose all your old clients on not be able to replace them (given that you have new clients paying the higher rate)

How much of a difference are you talking? Bringing it in line in one go may be unpalatable depending on the amount but in some ways better than being the person who is always increasing prices.

Generally speaking existing satisfied customers are good at accepting price increases. Give them some notice and explain why you need to do it and it should be ok as long as you are competitive in the market.