The funding programme for loft insulation has in the past been ECO - Energy Company Obligation. In the mid 2010s the eligibility was massively cut back and rates of insulation across the UK dropped off a cliff. Unless you are receiving a benefit (JSA, Universal Credit, etc etc) you won’t get ECO. Child Benefit is eligible for ‘dual measures’ - which I think is usually an insulation PLUS a new boiler under certain conditions. There are companies working on behalf of energy companies so you can simply google it to find companies. However beware the work can be sloppy - to get it signed off and get it recorded on a EPC there only needs to be insulation for 1 metre surrounding the loft hatch.
The top quality job for the loft is to incorporate air tightness and vapour control. Removing all insulation, putting heat/fire proof and air tight protection over downlighters and sealing around cable penetrations, and adding an insulated air tight loft hatch. Then you lay a vapour barrier membrane across and between the joists, and taping up the overlaps. Then after laying the insulatoin you put an airtight membrane over the top of the insulation to prevent air movement getting in or behind the insulation. Also ideally you would design wall insulation to be continuous with loft insulation. Example: Roof eaves: insulation & airtightness for a typical W. Yorkshire terraced house - YouTube
Most people don’t bother with this - I won’t in my current house - but this would be necessary for an AECB or Passivehouse standard retrofit.
Anyway the main step is adding up to 400mm of quilted insulation - mineral wool, glass wool and sheeps wool all have similar thermal properties. Sheeps wool and, I understand, some of the more expensive glass fibre, is nicer to handle. But the stuff permanently on special offer in B&Q is thermally as good as anything else. For all these materials you need to ensure it is not compressed, for example by objects resting on top. Building Reg in England requires a depth of 270mm, but the more the merrier. Joists are typically 6" deep = 150mm, so conventionally you put 1 150mm roll between the joists, and another 150mm roll across the joists. But you will get thermal benefit and good ROI on throwing an additional layer on top.
I experimented with rigid insulation but it is extremely difficult to get a airtight fit between the joists - avoid!
Important to make sure electrical cables have enough slack to rest on top of the insulation, otherwise you risk them overheating.
A detail I struggled with is at the walls where rafters meet joists and there isn’t 300mm of space so you risk a thermal bridge (cold spot) in the ceiling below by the wall, and you risk blocking ventilation which needs to be maintained around the rafters. See my comment about this here How to insulate a loft at the eaves
I have gone with these simple plastic inserts which maintain airflow while allowing you to push in more insulation than is otherwise possible. I’m planning to install on Monday so I’ll let you know if it doesn’t work out! Hambleside Danelaw HDURFT Universal Refurb Loft Tray Vent - Pack of 25 only £24.71
All this is from interest as a DIYer and AECB Carbonlite Retrofit course so professionals might provide more reliable advice.