7 day payment terms and getting tough with late payers

Hi, my partner and I run a small business and are invoices are constantly being paid late. Our terms are 7 days as stated in our T's & C's. We are looking at tightening up our invoicing procedure but want to be sure what we doing things lawfully. We are going to give notice to our regular clients about the changes:

1. Non payment of invoice on day 8 will result in a £50 fee (regardless of
the invoice amount - our invoices average £500)
2. Non payment after 30 days will result in additional fees and interest in
line with UK legislation.
3. We are looking at introducing a terms of engagement document which will
be sent to the client upon instruction. This can be completed and signed
online via a 3rd party company (e-sign or signable) By signing this
document the client is agreeing to our terms. If they do not sign then
our theory is that they are not the type of people we want to do
business with. GULP!

Does this sound ok, specifically the £50 fee?
Has anyone used e-sign for this kind of thing? Feedback appreciated.
Thanks.