There are so many different ways to approach commercial work. Here's one of them.
Don't jump into high volume work with both feet. Larger premises tend to have a person or department dedicated to purchasing. They are usually very good at it and their number one yardstick is typically price. You will rarely win on that front as the big players will employ perhaps minimum rate labour, cover their costs plus just a small percentage for the business profit.
So, try to specialise in certain sectors at a time. Don't go for the pubs in a chain, go for sporting and social clubs. Don't go for the Norwich Union (soon to be Aviva

) offices go for local solicitors and accountants.
So how do you get leads to these commercial prospects? Kitchen Sink Marketing

Engage your customers in conversation to build up that good tradesman relationship. If he/she goes to work, ask if it would be OK to drop a line using their name as a referee. Find out the name of the appropriate contact. Different professions/business' have different titles for the same role: Facilities Manager, Hospitality Manager, Housekeeping Manager etc. etc. So learn the appropriate titles too.
As a young business, residential work will supply you with a modest turnover with virtually no credit worries. Commercial work can be greater and more profitable but a cashflow nightmare. I was once told by someone who specialises in commercial work that you need enough cash to see you through 3 months in order to allow for the late payment of customers.
Get your presentations right and if you are invited to quote, jeans and trainers should be thrown out the window

Dress appropriate to the occasion.
Finally, if you have just £5k of Treatment Risk insurance, this will be totally inadequate for all but the smallest commercial work. You may need £millions. It needn't cost much either if you shop around.
Safe and happy cleaning

The Ken