Bear in mind, end of July to mid-August is school holiday time, so a lot of places will be more heavily booked up, or busier than normal. Mashu is indeed a beautiful place, but it's quite a trek. You'll need to get an express from Sapporo to Kushiro, which will probably take about 4 hours. Then change to a local train. According to a couple of my colleagues, it's better not to get off at Mashu station, but stay on the train until Kawayu station, as this is a small hot spring resort and has a bus service to the lake. Alternatively there are likely to be bus tours to Mashu from Sapporo, although you will probably be the only foreigners on a bus full of Japanese pensioners. Really, to see
Hokkaido well, you'd be advised to get a hire car or find someone who can drive you, if possible.
An alternative would be to go to Shikotsu-Toya national park, which is closer to Sapporo and as the name suggests encompasses both Lake Toya (Toyako) and Lake Shikotsu (Shikotsuko), both of which are beautiful in summer (Google them for pictures). You can get a very nice lakeside log cabin at Toya, for about 4-5,000 yen per person (sleeps up to 8). Nearby you can visit active volcanoes with steam and gas venting out of the sides and even go down into the crater.
Since you're a fellow Englishman, I might have been able to help you out, but as luck would have it, my wife is out of town for 6 bloody weeks from mid-July and she's taking the car with her.