I am a local Councillor and have been asked by residents if Parking restrictions, ie yellow lines which exclude commercial vehicle parking, ie vans.

Because of parking restrictions in the neighbouring borough, some people park vans sometimes for weeks in our ward to great annoyance to residents. Often parking in such a way that its difficult to get out of a drive.

Is there legislation in place to allow such restrictions?

You're a councillor. Don't you have officials who are paid to answer such questions?

If they work for parking departments, probably don't have a clue

Yellow lines restrict waiting by any motor vehicle
If large vehicles, goods vehicle restrictions can limit to them only
Othrwise you are into permit schemes.

If they are blocking driveways then get the police to act based on unnecessary obstruction.

Believe Bexley introduced single yellow lines, no parking 1100-1300, weekdays only.
Mostly to discourage commuter parking, so a resident tells me.
But it would also make van parking for weeks on end somewhat inconvenient.
Add enough 2 hour parking bays for people stopping home during their lunch break/visiting shops/etc...
Should move the parking problem a few streets along/to the next ward/borough.

The simplest way would be to have single yellow lines with different times on each side, say 10am-11am one side and 2pm-3pm the other. If a resident has a car parked they are presumably at home and can move it.

It wouldn't stop vans parking, and indeed it perhaps wouldn't be desirable unless you wanted to stop self employed tradesmen moving to the area. But it would stop long term parking.

The other option is to visit and offer to paint white bars across any driveway. They arent enforceable but they are free and quick, because you can charge residents for them.

The road traffic regulation act 1984 allows a council to apply to the department for transport for permission to place a non prescribed traffic sign. Your council (if it is the traffic authority) can for example, design a yellow no waiting sign that says "except for authorised vehicles" and seek DfT approval to use it. It would be a similar to the yellow sign part in this authorisation. Your traffic regulation order can define what is an authorised vehicle. It can define it by vehicle type or by certain users.

The other option is to impose a resident permit parking scheme with signs at all entry points that say "resident permit holders parking only past this point". Your traffic regulation order could then regulate what vehicle types to exclude from qualifying for a resident permit.

So yes there is legislation that can be used to achieve what many of your constituents want.