so if I was to stay in southend on Wednesday night then go back to london after the big bang on Thursday:
should i buy a return train ticket when i come from heathrow on wednesday? will that get me back into london cheaper then buying a ticket from Heathrow to southend then a separate ticket back to london on thursday?

I know when I was in England a few weeks ago I could not travel at peak times with my ticket back to Oxford? What are peak times? I am thinking I should be done with my business at the council between 1 and 2 and be ready to get on the train between 2 and 3. Will that put me at peak times and have to wait until after peak times?

Thanks for all your help. I am greatly appreciative.