I think that further restrictions on exercise are unlikely and would be unwise. The benefits from a marginally reduced risk of infection would, for most people, likely be outweighed by all sorts of negative health impacts associated with lack of daylight and exercise.
From my own observations (living in a large city, not London), it appears that the majority are abiding by the rules and socially distancing appropriately. Where this isn't the case then police and councils should by all means work together to tackle problem areas.
I think it's also important to bear in mind that the restrictions that the UK has in places are more typical of most countries than those of Italy and Spain which are outliers in terms of the strictness of their rules around exercise and there's no evidence that banning outdoor exercise has made a significant difference to their infection rates.
In sum, the risks of greater infection from outdoor exercise in accordance with social distancing rules are low or at worst uncertain. On the other hand, we can be quite confident that there will be significant, negative consequences of a prolonged ban on outdoor exercise.
One final thought on this: unless the data indicates that the existing measures have not had the desired effect on the trajectory of the infection rates, I can't see that there can be any justification for tightening restrictions. As of yet, insufficient time has elapsed since the introduction of social distancing measures to make that judgement.