My rights after a weeks employment

Since last year i have been an Letting Negotiator working in Hull. However in August, i saw a job advertised on the internet for a similar position to my current job only with better pay. So i subsequently applied. They had me for an interview the very next day, and within an hour of my interview they called me up and ofered me the job.

I worked my two weeks notice at my job in Hull, and started my new job on the 20th September. On Tuesday 28th September a close friend of my boss came into the office and asked to see if their was a job going. They arranged to go out for tea that very night for a chat. My day off in the week was a wednesday. I got a phone call wednesday morning from my boss, stating i was no longer needed as she was sacking me. I hadnt done anything wrong, had no warnings or anything.

I havent got a contract of employment from my new firm, am i entitled to claim for wrongful dismissal or loss of earnings, seen as i resigned from my old job to take up this new role?

It seems very wrong that a firm can just sack me like that after resigning from a good job, to come to them, and doing nothing wrong to get the sack.

Is their anything i can do?