Immediate payments for an accident claims

Yes, there are immediate payments made in an accident claim. However, these fall into the remit of your National Insurance and not your employers insurance
 
If you have an accident at work and are going to be off work for a period of time, you are entitled to statutory sick pay. This can be claimed from your employer if you need more than four days off work in a row and is payable for up to 28 weeks.
 
 If you are still off work after six months, you can make a claim for long-term invalidity or disablement benefit
 
To get Statutory Sick Pay (SSP), you should tell your employer that you are sick as soon as possible. You employer may have their own rules for when and how you tell them you are injured.
 
Links
 
Accidents at work Health and Safety Executive  Directgov