The Department for Transport does not have a policy on the number of traffic signs, including brown signs that direct visitors to their intended tourist destination. Although the Highways Agency's policy guidance documents on the use of tourist signing encourage highway authorities to consider the potential effects, no recommendation is made in relation to the number of signs.
Therefore no such research or evaluation has been undertaken.
The guidance documents TD52/04 (for the Highways Agency's all purpose and motorway trunk roads in England), and TA 94/04 (for local authorities in England on their local road network) can be found via the Highways Agencies website at:
http://www.highways.gov.uk/business/1162.aspx