Cyufjy

At the U.K. border in the Paris Eurostar, the border control refused my entry to the U.K. for below reasons.

1. Last nine and half months, too many ins and outs from the U.K.

I do not think there is a limit to visit the U.K. - multiple entry

2. Not booked a return ticket to my home country yet

We can visit and stay in the U.K. Maximum 6 months without any visa. If you do not know the return date, you can buy it later in the country.
Simply someone does not decide whether s/he can spend time in the U.K. for 4.5 months or 5 months unless "overstay" issue does not come up.

In this case, even with a purchased return ticket to my home country, will they still refuse my entry to the U.K.?

For the weekend trip, I visited Paris with only one small bag.
Even I want to buy flight tickets or any other means, WITHOUT bank card reader machines I cannot book tickets through online.

Moreover, my house keys in my home country are in my bag in London.
Even I go back to home country, I cannot enter my house.
No family is conscious, both Alzheimer's.

Thanks for your advice or some inputs in advance.

In general, visa free entry only allows what is permitted on a standard visitor visa. According to Standard Visitor visa, you cannot "live in the UK for long periods of time through frequent visits".

Although the chronology is not very clear, it appears the immigration officer decided your overall combination of number and duration of visits, combined with the lack of a plan to return to your home country on a specific date, amounted to living in the UK, not living somewhere else and visiting the UK. There does not appear to be a formula for deciding this, just an examination of your travel history and circumstances.

It is not simply a matter of number of visits. A business person based in Paris who has a weekly meeting in London would accumulate a lot of entries on Eurostar day trips, but obviously not be living in the UK.

It is possible, but very far from certain, that a visit to collect your belongings with a clear plan to leave in a few days, and a ticket home, might be permitted. You could avoid the risk of not being able to use the ticket by getting your belongings, at least the critical items such as keys and credit cards, packed up by wherever you have been staying and sent to you in Paris.

On 20 June 2018, I went to the UK to catch a connecting flight to Cyprus ( for finding a property there and few meetings there), and went back on 26 June this year.
On 10 Aug 2018 my friend and I came to Paris and on the last Sunday we were supposed to go back.

As I do not work in the UK, I showed my bank statements
to prove sufficient fund to travel, which showing the past activities for the last three months.

A business person (who is a non-EU citizen) living in Paris to make frequent visits to the UK by Eurostar is different from my case, because s/he resides in Paris(a EU memberstate).

I was supposed to ho back to home country on 3 Sep this year. I said so. But I had not purchased my exit ticket.
Usually for visa free nationals, unlike Chinese, Indians and other Asian country nationals, we are not always required to show the exit ticket from the UK for the special government arrangements.

Basically non-EU citizens but visa free nationals can visit snd travel in the UK up until 6 months.
Visiting the UK for 2-3 months does not constitute any breach of the immigration rules.

I think I need to make “entry clearance” at my home country