What "free" usually means
Bulky waste collection is genuinely free in a considerable number of places, and the phrase is also used heavily by commercial operators for whom it means a free quotation. Separating the two is most of the work, and the distinction is reliably visible: a public scheme names the authority, states what it will and will not take, and gives a booking route. A lead-generation page asks for a postcode and a telephone number before telling you anything.
Where collection is free it is normally free within limits. A fixed number of items per booking, a fixed number of bookings per year, kerbside presentation rather than in-house collection, and exclusions for the categories that cost most to process: fridges and freezers, tyres, paint and solvents, construction waste, asbestos. Reading the exclusions first saves the most time, because they are where a booking gets refused.
The three routes that cost nothing are municipal collection, reuse and charity collection. They suit different material. Anything with remaining use is better given away than disposed of, and a charity that collects will usually only take what it can sell, which is a useful filter on whether an item is genuinely still usable.