Normally, I would say that being entitled to another citizenship is a good thing. It can open doors otherwise not open to you, and allows you to live and work in more places around the world than you otherwise easily could.
But in this case, if you were to get a British passport, you might find that you no longer have Singaporean citizenship, as Singapore is very strict about not allowing dual citizenship.
While there are many people in Singapore who would gladly follow this path (largely to avoid national service), this would then mean that if you ever want to go to Singapore (the place you have called 'home' all your life), you would be treated as a foreigner. This means visas, work permits and perhaps applying for permanent residence in the future.
There is always the chance that Singapore looks badly on people who have given up Singaporean citizenship who then want to come back and live as a foreigner - and they may not even grant PR to such people.
I would have a word with an immigration lawyer in Singapore who would have experience in this matter. They can tell you the actual law and how it applies - don't listen to agents who would happily charge you a fee for each person to apply for a British passport, as well as all the other documents for your trip to the UK. Get solid legal advice as to how this will affect you all (your whole family), and what the actual requirements are.