If you had a mortgage before then you will need 20% deposit on the new house, I doubt the banks will budge on this. We're in a similar situation and in the process of mortagge approval. We had been approved in principle for an exception in Feb (LTI of 4.5x, we alread have >20% deposit), but the banks have all stopped issuing exceptions. However, the bank are considering future rental income of the property we own outright as part of our total income in the LTI calculation, which brings our approval amount closer to what we thought we would get with the exception.
With the current market I doubt we'll be buying or drawing down any time soon, but we figured it was worth continuing with the application and having it sorted just in case.