Actually, any highway maintained at public expense is owned by (vested in) the relevant Highway Authority (
s. 263 of the Highways Act 1980). In law a footpath is a highway or part of a highway. The courts have dealt with the extent to which s. 263 creates ownership - the case law is clear.
In London responsibility for the highway is shared between TfL, Highways England, the 32 London boroughs, and the City of London. Tower Hamlets Council could be the relevant Highway Authority for Brick Lane and therefore in law the owner of the footpath.
Who owns and runs the roads?
This is a surprisingly difficult question. There is a simple answer and a complicated answer.
The simple answer is that the public own and run them. Roads exist for the use of the public and are maintained by various government bodies at public expense. Roads in Great Britain can be divided into two categories for this purpose:
trunk roads and
non-trunk roads. Trunk roads (see
2.6 What is a 'trunk road'?) are nationally important routes, which are maintained by the national highway authority of each country (for example, the Highways Agency in England). All other public roads are maintained by local authorities — usually a city or county council. Roads in Northern Ireland are all maintained by the Northern Ireland Roads Service.
The complex answer is that roads — or more properly public highways — cannot easily be said to be owned by anyone. Often the land on which they exist actually belongs to whoever owns the adjacent land, and theoretically, rather like a path across a field, the land is theirs even if the right of way is superimposed on top of it. If the right of way were ever to be removed, or the road were ever torn up, the land would revert to its historical owner. However, a public highway is extremely difficult to get rid of and for all practical purposes the land between its boundary fences is treated as though it is owned by the authority that maintains it.
Land for new roads that were built more recently (from the early 20th century), and did not evolve from ancient pathways and tracks, is bought from the landowner by compulsory purchase before construction begins, and is then owned, outright, by the Crown.