That is true across the board. The 2030 RN includes two full-blown, angled-deck, gas turbine-powered aircraft carriers, an amphibious assault vessel, three LPDs, nine destroyers (all Type 45), 25 frigates (16 Type 26, 9 Type 23), nine nuclear attack subs (all Astute class), six AIP submarines (upgraded variants of the Upholders - the first four of that class served the RN until 2013, when they were transferred to the South African Navy) and a variety of minesweepers, patrol vessels and 35 vessels of the Royal Fleet Auxillary, as well as the four upgraded Vanguard-class missile submarines. Somewhat bigger than OTL, but not that much so.
You are correct that the Commonwealth core nations (UK, Canada, Australia, NZ, South Africa) do co-operate a lot. Between them, they can call up five full-sized aircraft carriers and over 100 destroyers and frigates, as well as a lot of amphibious assets. The RAF, RCAF and RAAF all have strategic airlift capability, and Britain and Canada have strategic bombers, which have in recent years come to be popular things, usually because the big aircraft can deliver a lot of ordinance, proved by operations in Afghanistan, India, East Timor, Zimbabwe and Korea. The RAF's strategic bombers are based off the American B-1, but as with the Canadian CB-1R, the RAF's Lancer B.1 uses a lot of locally-produced electronics and equipment. The B.1 replaced the Avro Vulcan B.3A in late 2025, allowing the Vulcan to be retired after nearly 70 years of service. RN aircraft carriers use Typhoon RN.3 and Tornado RN.5 fighters and strike aircraft and Viking ASW.1 anti-submarine aircraft, along with the ubiquitous Hawkeyes and Greyhounds, and Lynx Wildcat and Merlin helicopters.
The RAF is also somewhat bigger. The RAF's fleet uses the Eurofighter Typhoon for fighter roles, the Panavia Tornado GR.7 for strike duties, along with some Harriers, and a handful of Bombardier Crossbows for strike duties, usually in maritime strike roles. The RAF still uses heavily-upgraded variants of the E-3 for AWACS, though they, like most of the Commonwealth nations, use a variant of Airbus A330 as a refueling tanker, though the RAF still uses its Lockheed Tristars as well. For transport planes, the RAF relies on a fleet of Airbus A400Ms, delivered to the RAF between 1998 and 2001, and six C-17 Globemaster IIIs, delivered in 2006 and 2007. Three Bombardier CC-194V Ambassadors are also part of the RAF, operating usually as Royal Flights or transport for Britain's Prime Minister.
The British Army is about OTL size, though they have more gear. Britain's regular army ITTL is about 125,000 members, a time and a half the size of the Canadian Army, and they regularly compete against each other. Canada's products are fairly common among the British Armed Forces - Crossbow strike fighters and the Ambassador VIP aircraft serve the RAF, and Scorpion attack tiltrotors are used by both the Royal Marines and the British Army, and the RAF's Raytheon Sentinel is based on the airframe of the Bombardier Global Express, and was so successful at its role that Canada, Israel, Brazil, Japan and Australia bought them as well. The British are also buying the Tyranus R2/R2+ APC, having helped develop it, and they are developing a new tank to replace the Challenger 2, which will have a 152mm main gun and a APU in place of battery packs, which will likely replace the Leopard 2A6CA in Canadian service as well.