Join Date: Oct 2006
Location: London, UK
Programs: BA Gold, VS Silver, SQ Silver, IHG Plat Amb, Hilton Gold, Marriott Plat, Accor Silver, Radisson Prem
Posts: 16,873
You can't use miles to upgrade a travel agent booking. However, you could ask your travel agent how much they would charge to upgrade.
OLCI may present an upgrade price, which would be to the next higher cabin (so WTP in your case). The price is variable, but there is a POU (proactive upgrade) tracking thread somewhere here on FT (that I can't find at the moment) that lists likely prices.