You receive an additional +1 trade route for each continent that you have at least one Royal Navy Dockyard (including your home continent).
When they decided to be very heavy handed with england and not macedonia regarding free cities, this was actually the first thing that came to my mind. It's not a total fix to what they did to Pax, but it's a nice QoL buff.
I actually really liked England getting military units for settling cities and taking cities on other continents. I thought it was fun.
But anyways- we have 3 components of the civ here.
British Museum: cultural aspect
RNDY: economic/seafaring aspect
Her Majesty Victoria, by the Grace of God, of the United Kingdom of Great Britain and Ireland Queen, Defender of the Faith, Empress of India: Global imperial expansion aspect
I shall never apologize for giving proper recognition of a past Official Visitor of my College
So really, we need to look at the civ as a whole and not just the Pax ability. I think the british museum is fun enough and doesn't really need to be changed.
But RNDY and Pax are neither particularly strong- so we can either up the power found in them, or also look at their synergy.
Here's a rough sketch of some changes to keep England focused on being an imperial power that has an intercontinental empire in the age of civs like korea and the zulu. Numbers are rough examples.
On the Pax Side, preserving the focus of the British Empire in its colonial heyday is key. How that is achieved, could be military, could be other things. Beyond the free melee unit, another aspect is looking the Raj or colonial governance. Casa del Cont. has bonuses for governors on other continents; perhaps Pax could give something in this space. Since off continent cities suffer so badly from loyalty, I would put this piece here as well (and move it from the dockyard.)
Pax Britannica :
- Free melee unit when you settle a city on a foreign continent
- Governors on foreign continents grant an additional +4 loyalty to their city, and additional +2 loyalty to all of your cities within 9 tiles. [Amani's prestige promotion.]
- Governors on foreign continents grant +15% growth to their city.
- (Unlock Redcoats at military Science.)
HM's RNDY:
- +1 movement to all naval units built or upgraded in a city with this district.
- +1 gold for each luxury resource tile in cities on foreign continents. (Adds to the adjacency.)
- +0.5 gold for each specialty district in cities on your home continent. (Adds to the adjacency.)
- Provides +1 trade route capacity. Limit one per continent.
Why I chose these bonuses:
Foreign colonies are risky because:
- They are hard to defend
- Loyalty
- Also Loyalty
Foreign Colonies as nice because:
- They grant extra luxury resources
- They give new trade targets
The risks are addressed in Pax. #1 covers defense if you found colonies. Like Cape Town. If you're seizing cities, you presumably have an army, so I don't want to add too much power. #2 covers loyalty
if you invest your governance resources into your empire and #3 helps grow your colonies so they can generate more loyalty inherently. Remember, England had great success in actually getting colonial populations where other nations (like those total losers in France) failed. #4 is because we must paint the globe British Red

.
The Rewards are amplified by the RNDY.
#1 is obligatory naval boost. #2 is to motivate the actual reason for getting colonies in the first place: raw materials for industry and trade goods for the merchants. By giving an adjacency buff from the tiles directly without them actually having to be adjacent, RNDY can become very powerful. The Home continent bonus is there to let England get something out of the RNDY in case they cannot achieve their empire. We don't want to totally shaft them!
Together, these changed abilities would hopefully encourage England to create powerful colonial territories centered around their governors, rather than the occasional outpost for a couple luxes. For risking this venture, they are rewarded with extra trade routes, and powerhouse harbors generating a great deal of commerce for the empire.
Alternatives for Pax might include a reverse-teddy roosevelt of giving extra combat strength fighting on other continents, or making the colonial war CB easier to use (any civ with a capital on another continent could be the target) and grant extra combat strength/movement.
Alternatives for RNDY might include making a colonial bonus to be a direct boost to the luxury tiles themselves (like +1 production and gold to the tile.) Or increasing its trade route yield- it could grant +3 production domestically (instead of +1) and give +4 gold to outbound international trade routes, for example.