Once the seller has accepted your offer, ask them to take it off the market. They don't have to agree to this, but doing so will shut out other potential buyers.
Now you need to move fast - the seller will want to see progress so try to avoid any unnecessary delays in getting the surveys and other legal work done. Complete the lender's application form and send them the documents they require - this will include proof of your ID, evidence of your earnings, proof of your address over the last few months and your bank statements, so have these ready.
The lender will arrange for a valuation to be done on the property. If you are lucky enough to not need a mortgage, you don't have to get a survey done, though buying a property without one is not advisable and risky. If you are buying an older property, one that needs repairs or just for your own peace of mind, you could consider getting a more detailed survey done than the basic lender's valuation. Ask your estate agent or a surveyor at www.rics.org for a quote.
The lender will use the surveyor's Valuation Report and other information you provided to calculate how much it will allow you to borrow by way of mortgage secured on the property.