Can I use a wood-fired hot tub in a smoke control area?

Parts of the UK are smoke control areas. Outdoor barbecues, chimneys, fireplaces, pizza ovens are permitted for use in smoke control areas. However, local councils have a responsibility to investigate complaints of smoke and fumes that could be considered a statutory nuisance. In this event, an abatement notice may be issued, and failure to comply will result in a fine.

More information from the government:
Smoke control areas: the rules (external)