Firstly, your direct debit does sometimes go up during a fixed deal if you are consuming more than expected - that’s not prices going up, that just means the original estimation of your usage wasn’t correct. You only ever pay for what you use - it’s a false economy to have low direct debits and estimated bills. If you don’t have a smart meter, make sure you give regular readings to avoid getting hit at a later date.
Next, at the moment it’s probably best not to switch, the government price cap will protect you (fixed price deals are more expensive than the variable at the moment because the latter is protected by the price cap). Gas and power price curves do predict a fall in prices but not for a few months, so if you sign to an expensive switch and prices fall, you’ll pay over the odds. Best to just go on to the big standard variable rate. Energy company are under pressure because of the price cap - it has already been fixed and so they are losing money to the extent commodity prices are higher than the cap. So, we are all hoping for a warm winter - energy companies included. Little suppliers are going bust because they don’t always hedge their future purchases (hedging means that suppliers essentially ‘fix’ their commodity costs in advance - hence why some of the big names are now the cheapest).
If you swap into a new supplier, it’s probably best to stay with them tbh, due to government regulation, no energy company is making loads of money - but keep an eye on the market because if prices fall you might then get a better deal.
Btw, this has nothing to do with Brexit - it’s about a fall in generation.