The key word in your post is its 'citizen'. In UK, you can live and work for 6 years, then you can apply for ILR and a year later citizenship. In Singapore you can be high skilled and high income immigrant for 10 years with no criminal record but, you might never get the PR, let alone be a citizen. It might be easy 15 years ago in Singapore, not anymore. It's highly subjective and not transparent, there is also race based quota. UK system is not perfect but you can be in low income salary, as long as you meet the criteria, you and your family become citizen, and you are entitled to UK social services. So UK has far more percentage of people entitled to social services than Singapore.
Singapore is very selective in offering its nationality. So if you are the founder of Dyson or co founder of Facebook, you become Singaporean easily, and why wouldn't you want to do that, you pay such little tax on your wealth compared to UK or US. Singapore is a tax haven for wealthy.
Also you can't compare income of UK with Singapore. Singapore is located to a strategic location, near Malacca Strait, which is the largest strait in the world and very important shipping trade route. Singapore also values educational meritocracy, which makes its people more productive.
It's easy to help those in need if you have a lot of money and a smaller group of people in need of help.
But Singapore also has people from neighbouring poor countries working as house helps, who don't earn that much considering country's wealth.
Also, Singapore is not that foreigner friendly place ( especially since 2010) despite having 40% immigrant contributing to its economy. In recent years, Singapore government took measure to control immigration. A few years ago government increased the minimum salary requirement for issuing employment pass.
And during last 2 years, Singapore placed higher travel restrictions placed on foreign residents compared to citizens or PR. I read somewhere that Singaporeans were given a priority in vaccination programme and foreign residents were at the back of the queue.
So in my humble opinion, Singapore is not a good example for the UK to look up to in the matter of equality.
I would be more interested to discuss how to improve social and economical problems in current UK without comparing it to any other country as every country has different dynamics.
In my view, UK should emphasise more on education than it did in recent years - better funding, higher salaries to teachers and lower university fees.
If I were in the government, I would be lowering expense on defence, increasing tax for the wealthy and removing any perks for politicians ( I know it won't happen with Tory). We need some real patriotic politicians who deeply care for the country and its people, not the power hungry and lining their own pockets kinds.