I don't think that transfer fees are that much of an issue for them but the wage structure is. Most of their players (including Alli/Kane) are only on between £50,000-£100,000 per week and they seem reluctant to break the £100,000 mark for anyone.
Sure it's a lot of money for the average person, but if you are a player being offered 70k at spurs or 200k elsewhere it is an easy choice.
Kane could move tomorrow and get £300,000 p/w at any other top side and despite clearly enjoying himself at spurs at some point the extra 10 million per year he could be getting elsewhere is going to get very tempting if spurs don't start winning things