You'll probably save some money by taking the Ryanair flights from Stansted rather than the BA or Finnair flights from Heathrow. Typical return prices from Stansted are about �60-�70 (plus taxes). Equivalent fares from Heathrow start at about �170.
A taxi from Tampere airport to the rail station takes about 20 minutes. (For real economy, take the No.61 bus - about 40 minutes). Trains from Tampere to Helsinki run hourly and take 1 hour 49minutes for the journey. For comparison, a taxi from Helsinki airport to the city centre takes about 30 minutes; the express buses take about 50 minutes.
Chris