The government has pledged to set up a register of fishing rights, after widespread anger from small fishermen who say there is no way of discovering who owns the right to fish in the UK.

It would be the first time that the public, and fishermen, could find out which companies control the valuable rights to exploit the UK's fishing quota.

Fishing rights are distributed according to a formula set by the European commission, which sets a "total allowable catch" each year for each member state. The rights are then divided up among national fishing fleets by member state governments, and in the UK the quotas for each boat are determined based on historic fishing levels as well as the boats' capabilities, and the availability of fish.

However, this process is opaque and it is hard to know which fishing companies or individual fishermen are being handed quotas. The fishing rights are tradeable, so companies can sell them to one another in a complex web of commercial agreements.

The Department for Environment, Food and Rural Affairs (Defra) said the government was taking steps to remedy the situation, in response to the chorus of criticism. A spokesman told the Guardian: "We have recently held a consultation to look for ways of balancing the quota allocated to the larger industry and that of the under 10 [metres] fishing fleet. As part of this we have suggested a quota register and a web-based quota trading website to make this system more transparent. We are currently looking at the comments received and how we will take this forward."

The new register would, for the first time, show who owns the right to fish in UK waters.

At present, the rights are spread between a wide variety of organisations, many of which have nothing to do with fishing. Rumours even surfaced earlier this year that Manchester United plc and the Royal Bank of Scotland owned some rights. Both companies, when contacted by the Guardian, said they do not own any rights and have no idea why they are being cited.

Small fishermen are angry that the quota is being bought up in this way by large and untraceable companies. They say they are being priced out of the market, and that their own quotas are insufficient to make a living, while bankers and big companies are able to cream off profit from acquired rights.

Even parliament was unable to discover who owned the rights to fish and MPs demanded to know why the government was not monitoring the sale of the rights. The MPs, on the environment, food and rural affairs select committee, said the current situation was "unacceptable".

A spokesman for Defra said the detail of who owns the rights could not be disclosed at present owing to "commercial confidentiality".

However, this is at odds with the government's stance on other matters involving similar European Union regulations. Recipients of the Common Agricultural Policy, for example, are made public, along with details on the amount they receive under the policy.

In the UK, fishing quotas are allocated to three groups: producer organisations, made up of fishing boat owners; large vessels that are not part of such a producer organisation; and vessels of under 10 metres. Their rights are distributed in the form of "fixed quota allocations", which are based on the vessels' historic landings, calculated for a fixed period. Quota can be traded between groups, or among fishermen within groups, through temporary leases or on a permanent basis.

As well as putting fishing rights in the hands of large organisations unconnected with the sea, many older fishermen can keep their rights while retiring from fishing, selling their quota to others. But critics say these "slipper skippers" – so-called because they stay at home in their slippers while others go out to sea – are holding back working fishermen who cannot get access to a quota of their own.

Defra said the ability to lease and trade quota could "lead to a lack of transparency as to who may hold certain quota at a given moment in time". Its proposed register would make that clearer, providing a regularly updated snapshot of what trades had taken place and some details of the new owners of the rights.

Defra said it has no timescale yet for when the new online registry might be introduced.