Advice on the responsibilities of a Freeholder?

You could probably do it yourself, but you do need to tread carefully. My firm does some block management but, unfortunately, small blocks are just not viable due to the costs.
As the agent represents you, you need to make sure that everything they are suggesting is valid; if it is then you won't save too much money.
Our block owners struggle with the fact that we cannot turn a blind eye to H&S issues, especially those that are fire related. It can be expensive to deal with these matters, but it's in the freeholders' interests to get things sorted.

The main responsibilities for the freeholders are
1. to insure the building and have 3rd party liability cover.
2. Comply with fire safety regulations, see fire safety regulations 2022 and other legislation
3. Comply with the landlords obligations in the leases re external and internal redecoration and
4. maintenance of the building and communal areas.
Much can be done with common agreement ie setting a monthly figure, paid in advance, to cover insurance and ongoing expenses and build up a reserve for unforeseen expenditure.
You’ll always find that the organising is mostly done by 1 or 2 people. ie annual gutter cleaning if needed, getting quotes for works and buildings insurance
The threat of serving a s46 notice to any flat owner not paying their service/maintenance charge is enough to make them cough up.
Major works, anything over £250 per flat, can be sorted by a s20 Opt-Out agreement and majority agreement of freeholders

You only mention the internal communal areas but the freeholder is also responsible for the fabric of the building including exterior walls roof etc. and any garden or grounds

Reply to the comment left by Crossed_Swords at 15/06/2023 - 10:06
Yes, I didn't specifically mention the external fabric of the building but we are aware that is our responsibility. I think what bothered us particularly was a relatively large figure in the budget for 'internal redecoration' which is the very small lobby! Plus a figure for a WEEKLY test of the fire alarm system (I have seen a suggestion that we don't actually need an integrated fire alarm system). The gardens are owned entirely by the GFF leaseholder.

Ask the agent to justify the costs by providing quotes

If you have a fire alarm it must be tested but not necessarily weekly - could one of the residents do it?

Reply to Judith Wordsworth
You cannot’threaten’ a leaseholder with a I assume you mean a Section 146 Law of Property Act 1925 Notice. The actual wording of the lease covenant must be proved to have been breached and that means the landlord ie who is defined in the lease to whom service charge must be paid has complied with their obligations provided in the lease with regard to following proper legal demands in accordance with Landlord & Tenant Act and CLRA 2002.
. If the leaseholder disputes the sc then apply to FTT for a determination and only then can you take steps to retrieve the sc contributions.

Reply to the comment left by Crossed_Swords at 15/06/2023 - 10:06
I know our building, 8 converted flats, should have the fire alarm system tested weekly