Modern roofs are closed by design: fascia, soffit, dry verge, everything boxed in. A good many older Mildenhall roofs are not, and were never meant to be.
Those need a different approach, and the difference is worth understanding before anybody starts fixing mesh to things.

Open eaves
On a great many older buildings the rafter feet are simply exposed, with no soffit at all — the roof overhangs the wall and you can see up between the rafters. That is original construction rather than a defect, and it means the roof edge is open along its whole length by design.
Closing it means treating each rafter bay individually rather than running one board along, and it means keeping the ventilation the open eaves was providing. It is more work than a modern eaves and it is entirely doable.
Irregular verges and no undercloak
Old gable edges are frequently bedded straight onto the wall in lime mortar, without the undercloak a modern verge uses. The line is rarely straight, the tiles are often hand-made and irregular, and the gap behind them varies along the run. A standard dry-verge system does not fit such a roof and should not be forced onto it.
The answer is repair in the original material — lime rather than cement, which is both correct for the building and less likely to crack the way a hard mortar does against soft old brick.
No underlay
A great many old roofs have nothing beneath the covering at all. That changes the whole calculation: there is no second line of defence, so every displaced tile is a direct opening and closing the roof edge does not address the slope. Where this is the case it is worth knowing, because it explains recurrence that otherwise looks inexplicable.
Irregular junctions
Buildings that have been altered over generations have junctions that were made up on site, sometimes more than once. Roofs meeting at odd angles, a lower roof running into a wall at a slope, a chimney passing through a valley. Each needs handling individually rather than as a repeated detail.
The principle for all of them. Work with the construction rather than against it. A closure that fights an old roof will fail at its fixings and may damage the fabric on the way; one that respects the detail lasts and looks like nothing much.
Thatch, which is a separate matter
Thatch cannot be proofed in any of these ways. Where squirrels or birds are getting into a thatched roof the answer is wire netting over the roof, fitted by a thatcher, and it is a specialist job with its own considerations. It is not something to attempt as pest proofing.
Listed buildings and conservation areas
Where a building is listed, externally visible alterations may require consent, and concealed or reversible solutions are generally preferred. The right order is to check with the local authority conservation officer before committing, rather than afterwards. None of that delays the control work itself, which alters nothing.
Questions
Can an open eaves be closed at all?
Yes, bay by bay, keeping the ventilation. It is more work than a modern eaves and it is a normal job.
Should old verge mortar be repaired in cement?
Lime is the correct material for an old wall. Hard cement against soft brick tends to crack and can damage the fabric.
What about a thatched roof?
Wire netting fitted by a thatcher is the answer. It is a specialist job rather than pest proofing.
Squirrel Control Mildenhall
Squirrel control in Mildenhall is £280 fixed cost. Proofing work, where it is needed afterwards, is £180. Call 01502 630 122 and tell us what you have heard or seen.
For squirrel control in Mildenhall, call 01502 630 122, or read the Mildenhall squirrel control page.