Hc4361's link doesn't actually address the question directly, since the question relates to NOT having an adult present.
Although a Harvester functions largely as a restaurant, the law almost certainly regards the place as "exclusively or primarily used for the supply of alcohol for consumption on the premises". That means that, under Section 145 of the Licensing Act 2003, the licensee will be committing a criminal offence if "he allows an unaccompanied child to be on the premises at a time when they are open for the purposes of being used for the supply of alcohol for consumption there". (The definition of a "child", is specified as "an individual aged under 16").
So, if the question refers to a 15th birthday the law prohibits the presence of the person whose birthday it is. If it refers to 16th birthday the law only bars younger friends from joining that person.
However some licensing authorities may add additional provisions to the licence of a particular pub, relating to the presence of anyone under 18. Further Mitchells & Butlers (who run the Harvester chain) will have their own rules which their managers must observe.
I think that it's unlikely that M&B's rules would permit a person under 18 (not accompanied by an adult) from eating in their restaurants. The only certain way to check would be to phone the Harvester in question.
Chris