The single market in services is not as developed as the single market in goods, but it very much does exist.

If the UK leaves the single market and proceeds to trade with the EU under the terms of a free trade agreement, you would expect to see a reduction in services exports from the UK to EU. Some sectors will be more impacted than others.

https://www.cer.eu/insights/what-boris-johnson-eu-uk-free-trade-agreement-means-business

Anyway, I wrote a paper all about this. https://www.cer.eu/publications/archive/policy-brief/2018/brexit-and-services-how-deep-can-uk-eu-relationship-go