If the petition genuinely was about reducing avoidable animal suffering it would also want a referendum on banning factory farming and inhumane transportation in the UK. in which case I would definitely sign it.
Since it doesn't call for a referendum on these practices, the people who drafted it seem to be indicating they are only outraged about foreign cultural causes of unnecessary animal suffering, as opposed to being concerned about the issue of unnecessary animal suffering in general.
If the majority of people in the UK vote to halt only foreign cultural practices, that's fine with me. It will be similar to if the Saudis banned foreigners consuming alcohol in their country, because they find its consumption a distasteful foreign cultural practice. Though the Saudi princes are well- known for their love of alcohol and gambling, but they tend to only partake openly in both of these when they are abroad.