Currently there is a national scheme, called the Gigabit Broadband Voucher Scheme (GBVS), provided by the Department for Digital, Culture, Media & Sport central government department. In summary, as the name implies, this scheme is in place to assist with the funding to provide gigabit capable broadband services to residents and small/medium sized businesses (SMEs).
As part of this scheme vouchers are available worth £1500 per home and £3500 per business. These vouchers are made available to the service provider, not the individual residents/businesses.
In addition to the above, Nottinghamshire County Council (NCC) are providing a separate, top-up, investment as part of their Better Broadband for Nottinghamshire programme (further details here). As part of this scheme NCC are providing the same monetary amounts as above so bringing the totals to £3000 and £7000 respectively per qualifying address for the service provider.
These funds are to enable the service provider to fund the installation of the new infrastructure needed to provide the new service.
The service provider must be registered on the scheme and whilst there are many smaller companies providing this service the recommendation from NCC is that we use Openreach as part of their Community Fibre Partnership. The rational for this is that they are already working with them in other parts of the county and also importantly using Openreach will not tie/limit subscribers to a specific broadband provider for their service (see here for an explanation of how broadband is typically provided in the UK and where Openreach fit into the picture).
However the voucher scheme is ending very soon, so time is very tight!