Not if you are trying to get a new driving license from DVLA after a medical issue caused suspension of an old one. There is no online mechanism at all, either for the application itself, progress tracking or payment.
I don't drive, but if I were to guess I'd say that the painful parts you are going through are outsourced to some shit company designed to nickel-and-dime you.
One problem is that DVLA doesn't have an integrated back-end database that stores all driver data consistently. Some of their systems are new and whizzy (e.g. participating in an online auction for personalised number plates) but others are from the stone age.
Medical license application is also made worse because it requires the DVLA to interact with the NHS, using paper forms to request medical info and for the NHS doctors to request payment from DVLA for performing the medical reviews.