I haven't dined at the GF afternoon tea, but I'm sure someone will come along shortly with advice directly related to the tea.
However I have dined solo many, many, MANY times. And not just at fast food joints. LOL I remember the very first time I dined at a upscale restaurant I was super nervous. I knew the chef/owner and contacted him ahead of time to see if they could seat me with any other solo diners at the restaurant. He was super gracious in his reply. He assured me that I would not be bored or uncomfortable dining solo, but that if I was nervous about it I could always bring a book to read between courses.
I actually did download the kindle app for my phone and load up a book in case I needed it. But from the moment I was seated, I knew I wouldn't need it. The staff was clearly used to solo diners and they took their time with me and paid special attention to when I was finished with one course and promptly brought out the next one.
I used any down time to text Mr. Spuds and friends about the food I was having, the servers, the restaurant, etc. The time flew by! I was there for over 3 hours. And it felt like less than one hour.
From that point forward I was sold on solo dining! I have never had a bad experience. I encourage everyone to dine solo at a sit-down restaurant at least once in their life. It isn't for everyone I know. But it's so nice to just sit back and enjoy a meal at your own pace. I say go for it!!!!!