1. Take the London Underground (Piccadilly Line) to Russell Square or King's Cross/St Pancras. The journey takes about 55 minutes. Admission is 4 pounds. In addition, you can get a discount for handling the oyster card subway ticket!
2. You can also take Heathrow Express to Paddington Station. The whole journey takes only 15 minutes! One-way ticket 14.5. Then it takes about 10 minutes from Hammer Smith/City, Metropolitan or Circle Lines to Euston Square. Admission is 4 pounds.
All students in London can apply for the National Railway Student Oyster Photo Card. Subway tickets and bus tickets are discounted. You can still take a taxi. The price is around 60 pounds.
The nearest subway stations to UCL are Euston Square (hammersmith and the city, metropolis and ring road) and Warren Street (North Line and Victoria Line). Euston (North Line and Victoria Line) and Russell Square (Piccadilly Line). There are buses 10, 14, 24, 29, 73, 134 and 390 near UCL. UCL is close to euston, King's Cross Station and St Pancras!