"The results are very clear that more deer result in more ticks, and that deer management can be used for controlling ticks." This link takes you to a summary that provides links to the research papers.
See the related article that considers the 'Controlling Ticks by Treating Deer with Acaricides'. This idea has been around for over 10 years and was based on the success of treated White Tailed Deer in the USA. As the article indicates, there are practical issues that have so far prevented the treatment of Red deer in the UK. Some issues are not mentioned in the article: how to prevent individual deer obtaining an overdose of acaricide at treatment stations, how to keep acaricide out of the food chain and the impact of treatment with acaricide on the value of the venison.