Review of both parts:
I can see why some fans do not like this story because really it veers quite far from what you expect from the show. It is more like an Agatha Christie story than a Doctor Who story.
Some fans never liked the pure historical stories which had no real science fiction element (other than the Doctor and his companions arriving in the TARDIS) and that type of story was dropped way back in the mid 1960s with Season 4's The Highlanders being the last one (and not a great one). However, I loved many of the pure historicals such as Marco Polo, The Aztecs, The Reign of Terror, The Massacre, The Crusade and The Myth Makers. I loved them because of their quality but also as a story type because it is not just a space travel show or a futuristic show, it is a time travel show and showing adventures in history makes use of that which I think is an important feature that makes Doctor Who special.
I love pseudo historicals where aliens attack in Earth's past or whatever but I also feel it gives added diversity and interest to sometimes just have an adventure in the past. As long as a story has the Doctor, his companions and the TARDIS that is enough sci-fi for me as long as the story is high quality for an occasional different kind of story. This is a perfect example because it really is superb quality in every way in my opinion and the Doctor creates a really fun interaction within the period setting whilst the TARDIS is used in a lovely way adding a bit of an H. G. Wells touch which works well for the period.
The TARDIS takes them to 1920s England where the Doctor is mistaken for another doctor who is meant to be arriving to play cricket and attend a party. The Doctor demonstrates his cricket skills in a fun segment and then they attend for the masquerade party and find a girl who looks miraculously like Nyssa and discover a murder. A mysterious man steals the Doctor's fancy dress and there is a terrifying and brilliant cliffhanger before the second episode steps up the creepiness and the drama. I find the whole story fun, engrossing and beautifully done.
All the guest cast are superb with Moray Watson, Michael Cochrane and Barbara Murrey putting in fabulous performances as rich and interesting characters. The dialogue is wonderful with intelligence, charm and great delivery. The plot is excellent for a murder story and the additional Doctor Who elements just add the magic icing on the cake.
The mystery disfigured man adds a fantastic gothic horror feel and some really scary moments and the make up works really well.
The fire is done brilliantly, the period setting is magnificently evocatively created and there is lots to enjoy with little fun touches like Tegan dancing and Adric greedily devouring the buffet which I find hilarious. In fact, Tegan has never been better or more likable and Nyssa and Adric are the most fun they have ever been. Peter Davison puts in a strong performance as The Doctor and even the cricket playing adds an extra something different.
I love this story and the ONLY thing I find less than perfect is the coincidence of Nyssa looking exactly like Ann. Even that is really not a problem and has been done lots of times in Doctor Who, not always this effectively. The double role is achieved very well technically and works in the context of the story.
I cannot really fault this adventure apart from the coincidental lookalike/soundalike for Nyssa so I rate Part 1 as 9.5/10 and Part 2 it is just about a 10/10 in my opinion as I find it thoroughly enjoyable and so does my young son who is not usually interested in classic Who.
I feel it was heavily influential of the 10th Doctor story The Unicorn and the Wasp.
My ratings: Part 1 - 9.5/10, Part 2 - 10/10.