Although different water companies may have different policies, my understanding is this.
As carpet cleaning is for hygene as well as aesthetic reasons, water restrictions do not apply.
To receive dispensation to use your hose pipe you need to contact your water company.
There may be a requirement that you have a water meter.
It's always wise to check with the water company first. Whether you'll be able to get a definitive answer is another thing.
Safe and happy cleaning

The Ken