Depends how much money you've got - you can buy 'instant' mature hedging, already growing, but it does need extra care, particularly with water, and very good preparation prior to transplantation. More mature plants often don't settle so well and die though. However, if you've got a few hundreds to spare, that's worth investigating.

Otherwise, and this won't be cheap either, pots with large bamboo plants, but given a single large bamboo plant is likely to cost around £100, if you needed, say, 10 as a minimum... You could plant large bamboo straight into the ground, but you'd need a root rhizome barrier inserted first for most varieties these days.

You should also check that your local authority doesn't have strict guidelines about what type of hedging you can use before deciding.

Or the height of it......
smaller plants often thrive better than older ones....

What 'law' says that you cannot put up a fence? You will need planning permission for a front garden fence higher than 1 metre which is within a set distance from a public highway, otherwise it is 2 metres. I know some covenants prevent fences but these are normally unenforceable.

Ask the Planning Dept for advice. Its their stupid 'laws'
that most people find a way round. Say you are not able to keep trimming a privet hedge, which is what happens in years to come. A fence is tidier and easier maintenance.
Also with the recent gale force winds a fence protects plants.

If its a front garden it maybe dating back to when the houses were built, a friend has this where they live,
all the front gardens have to be kept below a certain height, it doesn't take into account ther rise in car ownership, there are cars everywhere, on the pavements, drives , verges, even on tight corners......you can't even See the front gardens, especially at weekends!
may be worth looking closely at the house deeds?

"If its a front garden it maybe dating back to when the houses were built"

My point is only the builder, at the time, could enforce the covenant. As the builder is no longer an interested party such covenants are unenforceable now as you need to be an interested party to enforce.

Its the council that makes the builder put this in the covenant though - they are the interested party as the garden adjoins their land. Some people get round it to some degree by a a flowerbed with a tall rose "hedge" eg Queen Elizabeth or even Rugosa, though these don't normally grow to five or six feet.

Botanic - if its a Conservation Area, all kinds of rules may apply - one up the road from me has privet hedges, and owners are not allowed to remove them and replace with fencing, nor must any hedge exceed 4 feet in height, and any hedge you may replace with has to have approval first...