It sounds as if there is no impediment to you moving the pension?
What kind of provider are you looking for?
As you have mentioned fees, and automatic investing, I would begin by investigating two providers to start with:
Vanguard - simple low cost investing with a limited range of Vanguard funds.
Wealthify - a subsidiary of Aviva.
It uses an automated process to create an investment plan based on your attitude to risk, investment amounts, and timescales for savings goals. A simple set of questions are presented for them to determine this online.
Investments are managed by algorithms and monitored by an investment team to keep them on track. The automated process keeps fees low.
I think these two would be a good starting point to see how they approach investing, and which one would suit you (if either). Their websites are both easy to use, and minimum contributions are low (£50 for both I think, either one off payments or regular investing).
If you are relatively inexperienced and don't want to choose your own funds, Wealthify will do this for you. Its site is slick and easy to use, with plenty of information and not too overwhelming.
They often have bonus offers for transfers at the start of the financial year - so perhaps have a look now, and wait to see what the offers are in April for an added boost to your balance if you decide to go down this route.
(Please do your own research, as I'm not a IFA. These are just my own ideas and experiences).