You’re going to find it pretty difficult to get in because there is a lot of competition for van work, especially the distance stuff as lots of people want the work. That being said if you don’t try, you will never get! Having the hgv qualification opens more doors because it shows that you are professional. Having the class 2 opens a lot of doors. Maybe general haulage would suit you? I have fibromyalgia and refuse any heavy work. Last year I did some work for Cobley’s which was 2 or 3 drops all over the place. I was working an average of 12 hrs per day and the rate was £12 per hour FOR DRIVING A 7.5! Not too bad! They wanted someone with a hgv in case they wanted to send me out in something bigger, but never did! Don’t hear me complaining.
If driving is what you want, go for it and give anything that comes your way a go. It’s all good experience. I don’t know what your personal circumstances are, but if it was me, I would be looking to sign with multiple agencies and be prepared to move about a fair bit until something permanent that’s the right fit comes along. A lot of people slag agency work but it’s a great way to test many flavours until you find one you like.
Good luck with whatever you decide