Yet, the veto records in the UN security council speaks volumes. The USA holds their hand over Israel, as they did for Apartheid South Africa.“Britain is a good friend of Israel, and our support for Israel and Israel’s security is unshakable. We are strong friends of Israel. There is a real opportunity with the end of bin Laden, and the Arab spring. This is a moment of opportunity to continue the work, and to defeat terrorism in our world and to continue the expansion of democracy, civil rights and freedom across the Middle East and North Africa.” David Cameron, UK’s Prime Minister
(translation: UK will be involved in the Middle East and in North Africa in the foreseeable future)
That said, you're right that their relationship is definitely strained due to the stance the general population of UK has taken in regards to Israel. But the stance of the population and the stance of the government who actually understands the tactical nature of its alliances are completely different things.
Since 1945, when the United Nations was founded, the Soviet Union and Russia have used their veto at the Security Council 120 times, the United States 76 times, Britain 32, France 18 and China only five.
From The veto and how to use it (BBC, 17 September 2003)In total, the US has blocked 36 draft resolutions on Israel.
The article says Russia (i.e. post-USSR) had only used the veto twice. Out of the 32 UK vetoes, 23 were together with the US, whereas all solo UK vetoes were on Zimbabwe.
More links on the topic (can't vouch for their veracity):
List of Security Council Draft Resolutions on Palestine Vetoed by the U.S. (Permanent Observer Mission of Palestine to the United Nations) - this list also details what the UK and other security council members did.
Use of the Veto on United Nations Resolutions by the USA
US vetos at the UN Security Council - List of UN Security Council resolutions vetoed by the USA, 1972 - 2002