The two old cannons are located inside Changi Naval Base. Since they are sited near the sea, you should be able to see it if you pass by on a vessel. However, I was not in the sea but on land. To be precise, I was on the grounds of the Navy Museum next door which is not a restricted area.
Nobody got the answer to the location correct although YG did come up with a good guess, i.e. Cliff House at Bukit Chermin Road.
Peter Stubbs was probably right when he said that the cannons looked very much like 68-Pounder Smoothbore cannons. Compare the cannons with the one in the photo below which is reproduced from the Wikipedia link on the 68-pounder gun:
The following passage of the 68-pounder gun is extracted from the Wikipedia link:
The 68-pounder cannon was an artillery piece designed and used by the British Armed Forces in the mid-19th century. The cannon was a smoothbore muzzle-loading weapon that weighed 95 long cwt (4,800 kg) and fired projectiles of 68 lb (31 kg). Colonel William Dundas designed the gun in 1846 and it was cast the following year. It entered service with the Royal Artillery and the Royal Navy and saw active service with both arms during the Crimean War. Over 2,000 were made and it gained a reputation as the finest smoothbore cannon ever made.
The gun was produced at a time when new rifled and breech loading guns were beginning to make their mark on artillery. At first the 68-pounder's reliability and power meant that it was retained even on new warships such as HMS Warrior, but eventually new rifled muzzle loaders made all smoothbore muzzle-loading guns obsolete. However, the large surplus stocks of 68-pounders were given new life when converted to take rifled projectiles; the cannon remained in service and was not declared obsolete until 1921.