Unless, as the case may be, either of the following paragraphs applies, the tenant's covenants in a bipartite lease can only be enforced by the landlord and the landlord is not under any obligation to enforce the covenants at the instance of a third party.
Some leases provide that some covenants are made not only with the landlord but also with the other tenants in a defined building. Such covenants would typically include covenants intended to be for the benefit of other tenants. So, if your lease contains a covenant by the tenant with both the landlord and the other tenants to do or refrain from doing certain things and they include something relevant, you have the standing to sue the chap above without reference to the landlord. "Something relevant" would be any one or more of the following:
(a) a covenant to keep the floors covered with carpet or other sound deadening material
(b) a covenant not to make excessive noise
(c) a covenant not to cause a nuisance or annoyance to other tenants.
Some leases provide that the landlord (this also may be something in the terms of service with the management company) will at the request of the tenant enforce the tenant's covenants contained in the leases of other units in a defined building. The provision is often qualified by requiring the tenant to provide security for costs and/or requiring assessment of the chances of success.
Absent of the above, you can fall back on the law of tort and sue for nuisance. The chances of success are perhaps lower than where suing for a breach of covenant relying on a well-drafted clause as it is necessary to show that the activity complained of is continuous, substantial and unreasonable.
In summary, you start with the covenants and you fall back on Environmental Protection Act 1990 and nuisance tort. As you can see Woody and I aren't quite in agreement (I don't think what you describe is bad enough yet to make a case under the Environmental Protection Act 1990), but this is probably a low cost option. It may be worth getting a solicitor to review the terms of your lease to advise - should cost less than £200