When you go there on Monday you should take meter readings and pass them to British Gas. If you tell British Gas that you are considering switching, they will tell you that they are best, you can save with their new tariff, etc. etc and you should ignore all this sales talk.
All the main suppliers have announced price increases and some of these will be applied in the next weeks, some will already have been applied. In order to compare everyone's price after their increase, you can either look up the applicable dates or wait a few weeks before using the price comparison tool. You will have a better idea of usage then as well.
The latter approach will also keep your partner happy, hopefully, as it goes along with the idea of seeing how things go with British Gas for now. If you do something that goes contrary to her wishes on something small like this, your relationship will not last.