This can and did happen under FPTP. You may not like the coalition, but that is the result of the FPTP system. A bit of background on the likelihood of coalitions is provided by full fact another useful article is Why AV does not necessarily produce more coalition governments. Nor does it help small parties to win more seats.

Extremists are unlikely to win seats as it requires 50% of the voters to make a positive vote for them. This actually seems quite unlikely for the BNP to gain a single seat in the UK parliament, and certainly not to have enough seats to justify them becoming part of a coalition government.

Finally I would suggest that the 'shameless governance' that exists as a result of the coalition government would only be worse if a single party was in government. It was not a coalition government that introduced the poll tax or invaded Iraq or even introduced tuition fees in the first place.

The version of AV that will be introduced is set out in the legislation that has been through parliament. There is not an option to vote for AV+, STV, or any other method - it is a straight choice between FPTP and AV.